Enhanced superconductivity in the compressively strained bilayer nickelate thin films by pressure

Domain: physics
Published: 2026-02-27
Editorial outcome: major_revision

Abstract
Recently, superconductivity with onset transition temperature (T onset) over 40 K was achieved in La3Ni2O7 and (La,Pr)3Ni2O7 thin films at ambient pressure due to in-plane compressive strain. However, the Tc in these thin films are lower than that of the bulk bilayer nickelates under pressure. Here we report the enhancement of T onset from about 30 K to over 48 K by applying hydrostatic pressure on the compressively strained bilayer nickelate thin films. The T onset firstly ramps up with pressure, then it slightly drops down after reaching the maximum T onset at about 48.5 K. Our theoretical calculations yield a cooperative enhancement of magnetic fluctuations between and within the layers and increased metallicity under pressure. These findings highlight the critical role of the interplay between interlayer and intralayer electronic correlations in bilayer nickelate superconductors and point to the potential of tuning Tc through controlled manipulation of the electronic structure and interactions.

Introduction
The discovery of superconductivity in bilayer nickelate La3Ni2O7 with transition temperature (Tc) exceeding the boiling temperature of liquid nitrogen has drawn enormous attention in both theoretical and experimental studies in the past 2 years. The electronic configuration in bilayer nickelate system is 3d7.5 (Ni2.5+) with dominantly the contributions of the eg orbitals, namely the 3d x2-y2 and 3d z2 orbitals near the Fermi level. Nowadays, nickelate superconductors are regarded as a new type of unconventional high-Tc superconductor beside the cuprates and lron-based superconductors. However, the requirement of high-pressure conditions to achieve superconductivity in the bilayer system has inhibited the investigation of the superconducting mechanism and potential applications of nickelate superconductors. Therefore, the pursuit of superconductivity at ambient pressure in nickelates with the Ruddlesden-Popper phase has been an ongoing task, and several promising routes, such as chemical substitution or strain effect, have been proposed in previous studies. Since the superconductivity in nickelate was first observed in an infinite-layer thin film with Tc about 9–15 K at ambient pressure, it is highly desired to explore ambient pressure superconductivity in La3Ni2O7 system via strains or fine tuning of the oxygen stoichiometry. Indeed, thin films of bilayer nickelates on different substrates have already been successfully fabricated, showing a promising route to achieve ambient pressure superconductivity. Very recently, signatures of superconductivity above 40 K in bilayer nickelate with a compressive strain (about −2%) at ambient pressure is achieved in bilayer nickelate thin films grown on SrLaAlO4 (SLAO) substrate and the superconducting properties can be strongly enhanced through combined chemical substitution and precise optimization during growth and post oxidation treatment. These findings have stimulated enormous interest, and several theoretical and experimental investigations have been carried out very quickly. The angle-resolved photoemission spectroscopy measurements on this type of films reveal the presence of the α and β Fermi surface sheets with the mixed 3d x2-y2 and 3d z2 orbital content, but without consensus about the existence of γ pocket which is purely derived from the 3d z2 orbital. The single particle tunneling spectroscopy measurements suggest the dominance of anisotropic s-wave gap(s) in the compressively strained bilayer nickelate films, supporting the Cooper-pairing scenario of bonding-antibonding s±-wave superconductivity. However, the maximum Tc observed in bilayer nickelate thin films so far is much lower than that in bulk samples under high pressure. One possible scenario is that the large compressive strain in ab-plane not only enhances the in-plane coupling to stabilize the ambient pressure superconductivity, but also increases the lattice constant in c-axis, thereby weakening the interlayer coupling along the c direction. In bulk La3Ni2O7, the flat band (γ band) with a large density of states just below the Fermi level with dominantly 3d z2 orbital character may play the essential role for the occurrence of high-Tc superconductivity. Therefore, the Tc in bilayer films might be further enhanced through chemical substitution or adding pressure to shorten the c-axis lattice constant.

In this work, we report the enhanced superconductivity on the superconducting bilayer heterostructure of (La,Pr)3Ni2O7/(La,Sr)3Ni2O7 on SLAO(001) substrate. At ambient pressure, the Tonset of the bilayer thin films is around 30 K (determined by using the crossing method as detailed below), and the superconducting properties are pretty stable in air. By applying pressure, the Tonset is monotonically enhanced up to 48.5 K at 7 GPa. With further increasing pressure, the Tonset is saturated and decreases slowly with increasing pressure, giving a dome-shaped superconducting region. More importantly, the normal-state transport measurements above Tonset show a transition from metallic to weak insulating behavior with increasing pressure. Aided by the theoretical calculations, our results imply crucial effect of interplay of interlayer and intralayer multiorbital electronic correlations as well as the metallicity in governing the superconducting transition temperature.

Results
Growth and characterization of bilayer nickelate thin films
According to the previous literatures, the superconducting bilayer nickelate thin films may have some diffusion of Sr2+ into the substrate-film interface. Therefore, to enhance the stability of the superconductivity in the films, we firstly deposit a 1.5 unit-cell (UC) of La2.85Sr0.15Ni2O7 layer on the SLAO(001) substrate, then deposit a 1.5 UC-La2.5Pr0.5Ni2O7 thin film, forming an artificial structure as illustrated by the schematic plot in Fig. 1a. The details for the growth parameters and heterostructure design can be found in Supplementary Note 1. The quality of the obtained thin film was confirmed by X-ray diffraction (XRD) 2θ-ω scans along the (00l) direction. The XRD data are shown in Fig. 1b. All the diffraction peaks from the films can be well indexed by the bilayer structure with the c-axis lattice constant of about 20.78 Å. This value is in good agreement with the previous studies on bilayer thin films and slightly elongated (+1.5%) compared to the bulk La3Ni2O7 (~20.45 Å) samples at ambient pressure. We also measured the Reciprocal space mapping (RSM) around the bilayer thin films (1017) and SLAO (1011) reflections (see Supplementary Fig. 1a), which confirm that the film is coherently attached to the substrate and thus compressively strained, with an in-plane lattice constant of about 3.75 Å. These results indicate that the film is compressively strained (−2%) in plane by the substrate, but the c-axis lattice constant elongates a little bit. By fabricating the (La,Pr)3Ni2O7/(La,Sr)3Ni2O7 heterostructure (LSP327) with a compressive strain and precise in-situ ozone annealing, we can obtain superconducting nickelate thin films with the bilayer structure. Interestingly, our films are quite stable in air, which maybe induced by the specially designed heterostructure (see Fig. 1d and Supplementary Fig. 2).

Figure 1d displays the temperature dependent resistivity ρ(T) of a variety of thin films. All the measured thin films exhibit good metallic behavior and clear superconducting transitions at ambient pressure. The Tonset varies from 21 to 34 K and most of the transitions have a resistivity drop over 90% at 2 K. In this paper, we define the onset of superconducting transition (Tonset) as the cross-point of the linear extrapolation of normal state and the transition region with 80–90% of the normal-state resistivity. We also measured the ρ(T) curves for LSP327 films under different applied magnetic fields (see Supplementary Fig. 1b). The resistivity transitions are gradually pushed to lower temperatures by magnetic field as expected for a superconducting transition. The magnetic field dependent Hall resistance (RH) of LSP327 thin film was measured between 40 and 200 K (see Supplementary Fig. 3) by using the standard five-probe method on the thin film with a size of 3 mm × 1.5 mm as shown in the inset of Fig. 1c. Since the sample size is relatively large with a rectangular shape, and the electrodes for applying the current is parallelly made in the two terminals, therefore, the current is supposed to be uniformly applied on the thin films. As shown in Fig. 1c, the calculated Hall coefficient (RH) is positive at measured temperatures and decreases with increasing temperature. Such behavior may indicate the multiband nature or correlation effect of the superconducting bilayer nickelate thin films in the normal state, and is consistent with previous results on bulk crystals and undoped La3Ni2O7 thin films. Note that a negative RH was observed in some doped bilayer nickelate thin films previously and an electron-hole crossover of the RH was reported in superconducting La3-xSrxNi2O7-δ thin films with different oxygen content. Therefore, the positive RH in our bilayer LSP327 thin film may be due to the special doping concentration and oxygen contents. More importantly, we find that the superconducting transition of the grown films are very stable in air. For some films, after being placed in air for more than 1 month (see S1 and S2 in Fig. 1d), apart from a slight increase of the normal-state resistivity, the superconducting transition still looks very sharp without degeneration. Without this kind of heterostructure, the films are pretty easy to deteriorate in air, showing fragility of superconductivity, and it is hard to do the subsequent transport measurements especially under high pressures. However, the LSP327 thin film samples reported here are air-stable, which enables us to conduct subsequent investigation on the transport properties of the bilayer nickelate thin films under pressure in different labs with different high-pressure cells.

Evolution of Tc and normal-state transport behavior under pressures
As reported previously, the superconducting bilayer nickelate thin films were grown on a SLAO substrate with a compressive strain (about −2% compared to bulk crystals), which consequently leads to around +1.5% elongation of the c-axis lattice parameter comparing to bulk samples. This will in turn lead to the elongation of out-of-plane Ni-O bond length, thereby weakening the interlayer d z2-orbital coupling. Naturally, one possible approach to increase Tc in bilayer nickelate thin films is to reduce the c-axis lattice constant through pressure or chemical doping. Figure 2a presents the ρ(T) curves of LSP327 sample (S1) under various pressures up to 2.6 GPa measured in a piston-cylinder cell (PCC) with Daphne 7373 as the pressure transmitting medium (PTM). The normal-state resistivity gradually decreases with increasing pressure, and the residual resistivity at 2 K decreases progressively. As shown in the inset of Fig. 2a, the zero resistance is reached at around 2.3 K above 2.0 GPa, indicating the better connection of the superconducting paths in LSP327 thin films under pressure. The little step at about 173 K at ambient pressure may be due to an instant temperature instability in the warming up process. Figure 2b presents the enlarged view of the ρ(T) curves in the temperature region near the onset of superconducting transitions. The definition of Tonset is illustrated in Fig. 2b. It is clear that the Tonset is monotonically enhanced from 29 to 35.4 K with increasing pressure up to 2.6 GPa, giving a slope dTc/dP of about 2.46 K/GPa. This value is much larger than that reported in the infinite-layer nickelate under high pressure. We have also conducted the transport measurements on another thin film (S2) under high pressure and the results are presented in Supplementary Fig. 4. The similar evolution of ρ(T) curves and Tonset under pressure indicates that the enhancement of superconductivity in the thin films is intrinsic and reproducible.

Figure 2c presents the full range ρ(T) curve of a LSP327 thin film at 2.6 GPa. The curve with red color is the fitting curve using ρ(T) = ρ0 + ATn from Tc to 200 K, and the fitting yields n = 1.79. In the temperature region above 200 K, the ρ(T) curve instead shows a T-linear dependence (n~1) as indicated by the blue line. To see the evolution of the normal-state transport behavior above Tc, we also performed the similar fitting on other ρ(T) curves under different pressures and show the evolution of fitting parameters with pressure in Supplementary Fig. 5. The fitting results indicate that the normal-state transport behavior shows typical Fermi-liquid behavior (n~2), but a slightly decrease of n appear with increasing pressure, which indicates the gradual involvement of other exotic scattering or strange-metal behavior under high pressure. Considering the fact that the strange-metal behavior (n is close to 1) is widely observed in bulk bilayer nickelates under pressure and infinite-layer superconducting films, we may expect that the normal-state resistivity would show a T-linear behavior when the Tc approaches its optimal value. Pressure dependent RH measured at 40 and 60 K shows roughly a declining trend with increasing pressure as displayed in Fig. 2d and Supplementary Figs. 6 and 7. In a single band model, such behavior would indicate that the carrier concentration increases upon applying a pressure. Considering the multi-band nature of bilayer nickelate superconductors and potential role of oxygen deficiency, a quantitative interpretation of the RH data here is very challenging. As we show below, the nonmonotonic change of RH under pressure can be explained by the increasing size of the γ-Fermi pocket with pressure. Anyway, the pressure can indeed enhance the itinerancy of the charge carriers, leading to a better metallicity in the normal state in the pressure region up to 2.6 GPa.

To further study the evolution of Tc in LSP327 bilayer thin film under higher pressures, we performed high-pressure resistivity measurements under various hydrostatic pressures up to 13 GPa using a cubic anvil cell (CAC) apparatus. This technique was successfully used in enhancing the superconducting transition Tc of the infinite-layer nickelate thin films. Figure 3a and Supplementary Fig. 8a show the ρ(T) curves of two LSP327 thin films (S3 and S4) measured with glycerol and Daphne 7373 as the liquid PTM, respectively. The slight variation of absolute resistivity at 0 GPa for different experimental runs is inevitable since there is certain sample dependence in different films, and a slight degradation occurs when polishing the substrate of the thin films for the CAC measurement. Before getting to the enhanced superconductivity under higher pressures, firstly, we focus on the normal-state resistivity above Tc. As shown in Fig. 3a for sample S3, the room temperature resistivity (ρ293K) shows a non-monotonic evolution with increasing pressure, it exhibits a gradual decrease with pressure when P < 7 GPa, and then it shows an increase above 7 GPa. For another sample S4, by using the Daphne 7373 as PTM (see Supplementary Fig. 8), the ρ293K first increases when the pressure is increased from 0 to 2 GPa, and then it decreases with pressure increased from 2 to 4 GPa. With further increasing pressure, it keeps a monotonic increase until 12 GPa. The nonmonotonic change of the normal-state resistivity shows different behavior in different experimental runs (see Supplementary Fig. 9), which is similar to the case in the doped infinite-layer nickelate thin films under high pressures. In these infinite thin films, defects or disorders were observed and are supposed to dominate the electron scattering processes. There are several extrinsic factors that can affect the absolute resistivity of thin films when pressure is applied, for instance, the solidification of PTM, the changes of the electrode contact, defects or disorders generated by pressure, etc. Therefore, we attribute the change of the magnitude of normal-state resistivity in our thin films under pressure to extrinsic reasons. More discussion concerning the abnormal change of normal-state resistivity under pressure can be found in Supplementary Note 2.

Above about 9 GPa, the normal-state resistivity above Tc for experimental runs on two samples (S3 and S4) shows similar metal to weak insulating transitions in low temperature region, and the insulating feature becomes more and more obvious as the pressure is further increased. Despite the variation of normal-state resistive behavior, the superconducting transition can still be clearly observed, which shows an enhancement of Tc with pressure up to around 7 GPa, then it saturates or slightly drops down at higher pressures.

In order to clearly track the evolution of the superconducting transition under high pressures, we show the enlarged view of temperature dependence of resistivity of S3 near onset superconducting transitions and extracted the Tonset at each pressure for samples S3 and S4, as displayed in Fig. 3b–i and Supplementary Fig. 8b–h. We can see that the Tonset exhibits a nonmonotonic evolution with increasing pressure. The definitions of Tonset are the same as that in Fig. 2b. For sample S3, the ρ(T) shows Tonset ≈ 32.4 K at ambient pressure, and the residual resistivity at 1.5 K can be seen clearly, which should be ascribed to the small-sized sample (typical size of 0.6 mm × 0.3 mm) with prominent inhomogeneity for high-pressure measurements. Upon applying pressure to 2 GPa, we can observe perfect zero resistance with Tzero ≈ 2 K and Tonset ≈ 38.3 K for sample S3. The superconducting transition temperature of sample S3 increases to Tonset ≈ 41.3 K and Tzero ≈ 2.4 K at 3.5 GPa, and Tonset ≈ 47.1 K and Tzero ≈ 5.3 K at 5 GPa. With further increasing pressure, we can see that the zero-resistance state cannot be achieved above 7 GPa, but the thin film still exhibits a clear resistivity drop even at 13 GPa. The optimal Tonset ≈ 48.5 K at 7 GPa can be seen in Fig. 3f. We want to note that that if we follow the temperature dependent resistivity curve and determine the temperature where the resistivity starts to drop, the highest temperature of about 61.5 K is observed as shown in the inset of Fig. 3a, which indicates that there is a potential for further optimization of the Tc under pressure in the nickelate bilayer thin films. In contrast, the superconducting transition is considerably broadened with a large residual resistivity for sample S4, and it maybe ascribed to the presence of substantial stress/strain induced by the solidification of Daphne 7373 upon compression and cooling down. However, even the transition becomes broad at high pressures above 9 GPa, we can still track the onset of superconducting transition, and its evolution is consistent with that of sample S3 (see Supplementary Fig. 8). In addition, the slight semiconducting like feature in the normal state above 9 GPa is intriguing. Such a weak insulating behavior seems not be induced by the solidification of the PTM since it occurs in the same way for the two runs of measurements with different PTM (and thus different solidification pressures/temperatures), and this insulating feature was not observed in previous studies on the pressurized effect on the infinite layer thin films, although the PTMs used are the same. We may argue that the weak insulating behavior above Tc at high pressures is an intrinsic property of the bilayer nickelate thin films. The insulating feature occurs at the same pressure when the Tc starts to decrease with pressure and the ρ(T) curves in this region can be fitted by the ρ/-lnT relation (see Supplementary Fig. 10). Such behavior has been reported in the underdoped cuprates. Note that the weak insulating behavior is absent in bulk crystals under pressure, this discrepancy may be because of different electronic structures in bulk samples and thin films. In thin film form of nickelate superconductors, the weak insulating behavior is also observed in Sr-doped La3Ni2O7 with dome-like superconducting region. Therefore, the weak insulating behavior in present bilayer thin films under high pressure maybe induced by some intrinsic origins, for example the gradually enhanced correlation effect which provides the tendency for the formation of a density wave order, probably associated with the shift of the γ-pocket with a flat band feature.

Tc-P phase diagram and theoretical understanding
Figure 4 shows the pressure dependence of superconducting transition Tc obtained from the high-pressure resistive measurements on LSP327 thin films (S1-S4) with different high-pressure cells and PTMs. As can be seen, the phase diagram depicts explicitly a delicate evolution of superconducting transition, which shows clear difference to the results of La3Ni2O7-δ bulk samples. With increasing pressure gradually, Tc(P) shows pronounced positive pressure effect (dTc/dP ~ 3.3 K/GPa) and Tonset exhibits a rapid increase from about 30 K at ambient pressure to 48.5 K at 7 GPa, and then it decreases slowly to 42.8 K at 13 GPa, which features a dome-shaped superconducting phase diagram with the maximum around 7 GPa. The optimal Tonset and the critical pressure in the LSP327 thin films are lower than the corresponding values in its bulk counterpart under a high pressure, which would imply a significant difference of electronic states under pressure in bulk samples and the compressively strained thin films. This can get some reflections from our theoretical analysis as follows.

In Fig. 4, we also mark the behavior of the normal-state resistivity with different colors. Surprisingly, the maximum Tonset corresponds with the threshold pressure for the distinct normal-state behaviors very well, namely the crossover from metallic to weak insulating behavior in low temperature region. Note that the solidification of PTM will not affect the electronic structure of the thin film since it merely introduces disorders or defects in the film, thereby affecting the magnitude of the normal-state resistivity.

To get insight into the electronic origin of the Tc evolution, we first perform density functional theory (DFT) calculations for the strained thin films as a function of pressure. In particular, we assume that external pressure acts on a lattice already clamped by the substrate, so the in-plane lattice constants and the in-plane Ni-O-Ni bond angle remain largely fixed while compression is mostly accommodated along the out-of-plane direction and can be modeled by the variation of the out-of-plane lattice constant c. Thus, our hypothesis is that in thin films pressure mostly affects the c-lattice constant, while keeping in-plane Ni-O-Ni bond angle fixed. More detailed discussion can be found in Supplementary Note 3. On the contrary, in the bulk crystals, there is a remarkable correspondence between the in-plane Ni-O-Ni bond angle and the Tc value once the structural transition to the I4/mmm phase takes place. Note, in compressed thin films the in-plane bond Ni-O angle is more bent than those achieved under hydrostatic pressure, correlating with a lower Tc. Thus, the effect of the hydrostatic pressure on the bulk and thin films is largely different. To be specific, we compute the electronic structure for ambient pressure, c0, and study additionally the cases of 1.5%, 3%, and 5% reduced c by using c = c0 − Δc. In the next step, we develop an effective low-energy model consisting of two 3d x2-y2 and 3d z2-orbitals located on two sites in a bilayer, which is obtained by maximally-localized Wannier downfolding. The three-dimensional effective band structure is only shown for the ambient pressure, as well as the 5% case in Supplementary Fig. 11a. Three bands cross the Fermi level in our model independent of the applied pressure. They are denoted as α, β and γ bands, following the standard nomenclature. The α and β bands are of mixed 3d x2-y2 and 3d z2 orbital character with dominant contribution of the former near the Fermi level. In contrast, the more flattish γ band is of 3d z2 orbital character near the Fermi level. To include the effects of the electronic correlations, we perform the rotationally invariant slave boson approximation, using U=7eV, V=1eV. The renormalized band structures for each pressure are shown in Supplementary Fig. 11b and the resulting Fermi surface for ambient and 5% reduced lattice constant c are shown exemplarily in Fig. 5a. Observe that the largest effect of the pressure for the Fermi surface and the bandwidth occurs for the γ pocket. This is expected due to the strongest effect of the c-lattice variation on the 3d z2 orbital. The γ band shifts upwards with respect to the Fermi level and increases its bandwidth (see Supplementary Fig. 11). This upwards shift corresponds to a charge flow from 3d z2 to 3d x2-y2 orbital with increasing pressure and reflects the reduction of the crystal field splitting (for Δc = c0 = 0, 1.5, 3, 5%: Δcf = 541, 391, 316, 184 meV). The crystal field splitting is also influencing the leading instability in the linearized gap equation based on RPA spin calculations. In addition, we have also performed Hall coefficient calculations within standard Boltzmann theory using the obtained electronic structure (see Supplementary Fig. 12). In the oxygen-rich (clean) case, the Hall coefficient at ambient pressure is slightly negative, consistent with the results of ref. 45. Upon increasing pressure, however, the Hall coefficient turns positive, reflecting the stronger contribution of the γ-band at the Fermi level. This seems to be opposite to the observation of a positive Hall coefficient in our present thin films, which maybe explained by the presence of some oxygen deficiencies in the samples.

In addition, there is an overall increase of itinerancy of the bands, which is due to stronger hybridization of 3d x2-y2 and 3d z2 orbitals and a charge flow from 3d z2 to 3d x2-y2 orbital upon pressure. The increased metallicity is illustrated in Fig. 5b where we plot the quasiparticle weights (residue) of the two orbitals for various pressures. This is consistent with the Hall coefficient data below 2 GPa as shown in Fig. 2d, indicating stronger metallicity of the normal state upon applied pressure. However, the observation of weaking insulating behavior under higher pressure seems contrast to better metallicity proposed from the theoretical results above. As we will discuss below, the weaking insulating behavior may originate from enhanced correlation effect under pressure, namely, the formation of a possible density wave order due to the shift of the γ-pocket with a flat band feature.

Next, we turn to the spin susceptibility as described in Fig. 5 and Supplementary Figs. 13 and 14, and the calculated bare spin susceptibility without doping is depicted in Fig. 5c, d. Both, even (in-plane) and odd (out-of-plane) spin components are shown χe = (χbb + χaa)/2 and χo = (χab + χba)/2. Here, for example, the in-plane χbb describes contributions due to the scattering from a bonding to a bonding band. The odd channel essentially describes the scattering between bonding and antibonding bands. Consequently, strongly dominant spin fluctuations in the odd channel do naturally provide the pairing glue for the bonding-antibonding s±-wave. An enhancement with decreasing c in the odd channel is seen, when the slave boson quasiparticle weights, which are shown in Fig. 5b, are included. Note that the renormalization for the 3d z2 orbital is stronger than that for the 3d x2-y2 orbital. The difference in the orbital renormalization, however, is reduced through reduction of c-axis lattice constant. However, the even spin fluctuations are also significantly sensitive to the changes of the c lattice constant. Especially, a domelike behavior is seen for the qe1 and qe3 peaks, which is consistent with the experimental observation shown in Fig. 4.

Within our theoretical description, the external pressure is modeled by the reduced c-axis lattice constant, while the in-plane lattice constants and the in-plane Ni-O-Ni bond angle remain largely fixed by the substrate. Nevertheless, already this change modifies both the in-plane and the out-of-plane magnetic response, which makes it challenging to single out the main effect responsible for the increase of Tc with pressure and even make further assessment on the most probable symmetry of the superconducting gap. We remind that the main candidate solutions for the superconducting gap in the bilayer nickelates are either bonding-antibonding s±-wave or d-wave (either dxy or dx2-y2) gap structures. At the same time, we can identify universal features in the electronic response upon the reduction of c-axis lattice constant only, which are (i) increased hybridization between 3d z2 and 3d x2-y2 orbitals (ii) larger itinerancy of the pressurized system, and (iii) enhanced antiferromagnetic spin fluctuations both in the in-plane and out-of-plane channels. Moreover, these effects quickly saturate upon larger reduction of the c-axis lattice constant explaining why no further increase of Tc and even its reduction is observed. To see that these universal features stay the same for the slight variation of the electronic structure we repeat the same calculations by doping of 0.1 holes or 0.2 holes per Ni atom assuming potential doping effect of the substrate, as shown in Supplementary Figs. 13 and 14. Remarkably, the universal features we observe for non-doped compound stay the same.

Methods
Sample preparation and characterization
The nickelate thin films with bilayer structure were grown by pulsed laser deposition technique using (001)-oriented SrLaAlO4 single crystal as substrate. The growth process and parameters are similar to that reported previously. The details about the synthesis process of bilayer heterostructure of La2.5Pr0.5Ni2O7/La2.85Sr0.15Ni2O7 and post annealing parameters are described in Supplementary Note 1. The XRD 2θ-ω scans and RSM were obtained using a Bruker D8 Discover diffractometer with a Cu Kα1 radiation source (λ = 1.5406 Å). The crystal structure was modeled using VESTA software. The temperature-dependent electrical resistivity and Hall coefficient measurements at ambient pressure were carried out on a physical property measurement system (PPMS, Quantum Design) using gold wires as electrodes.

High-pressure measurements in PCC and CAC apparatus
Standard four-probe method was employed to measure temperature-dependent resistivity of the LSP327 thin films with the electric current applied within the ab-plane. Resistivity measurements with pressures below 2.6 GPa were carried out in a PCC apparatus (HPC-33, Quantum Design). The sample was immersed in a liquid PTM of Daphne 7373 in a Teflon cell. Hydrostatic pressures were generated by a non magnetic BeCu/NiCrAl piston-cylinder cell. The applied pressure at low temperature was determined by the shift in Tc of a high quality Pb single crystal. The Hall resistance at ambient and high pressures (below 2.6 GPa) was measured using a five-probe method and the electrode configuration is shown in the inset of Fig. 1c. For measurements at higher pressures, we employ a palm-type CAC to measure its resistivity under various pressures up to 13 GPa with the glycerol as the liquid PTM, and to 12 GPa with the Daphne 7373 as the liquid PTM. The pressure values inside the CAC were estimated from the pressure-loading force calibration curve pre-determined by measuring the Bi and Pb at low temperatures. The resistivity values in CAC at 0 GPa is a little bit larger than that in PCC at ambient pressure, this may be due to the slight degradation of the film when we polish the substrate of the thin film to lower its thickness for the CAC measurements.

Theoretical calculation
To get insights into the electronic states of the thin films, DFT in the local density approximation within a mixed-basis pseudopotential framework is applied. The application of pressure is modeled by variation of the out-of-plane lattice constant and fixed in-plane lattice constant within a bulk-like setting. To be specific, we use c0 for ambient pressure and study additionally the cases of 1.5%, 3% and 5% reduced c by using c = c0 − Δc, while keeping the in-plane parameters fixed.

In bilayer systems, the electronic states in band space can be approximately diagonalized by introducing bonding and antibonding states c±,k = 1/√2 (c1,k ± c2,k), where c1,k and c2,k denote the annihilation operators for an electron in layer 1 and 2 with momentum k, respectively. Within the description of the two orbital bilayer model, the α and γ bands belong to the bonding subspace whereas the β band is of antibonding character. Scattering events can be classified in those which happen within the bonding or antibonding bands and those which happen between both subspaces. The even and odd susceptibilities are defined by χe,o = 2(χ11,11 ± χ11,22), where orbital and spin indices are omitted. The physical spin susceptibility in the paramagnetic state is determined by even and odd channels as χspin(q) = Σμ1,μ2,μ3,μ4 [χeμ1μ1,μ2μ2(q)cos2(qz/2) + χoμ1μ1,μ2μ2(q)sin2(qz/2)], where q = (q, ω) and the sum μ1,2 run over both Ni eg orbitals. The bare susceptibility is calculated using the renormalized band structure. Furthermore, the slave-boson quasi-particle weight is dominated by the diagonal part. These diagonal elements Zμ can be used as Zμ1 Zμ2 Zμ3 Zμ4 χe,oμ1μ1,μ2μ2(q) to account for the orbital selective quasiparticle weights. While the spin susceptibility is only shown along the high-symmetry path in the qz = 0 plane, the full k dependence of the band structure is included in the calculation. To be specific, a 200×200×25 k-mesh and bulk filling has been used to obtain the results in Fig. 5. To account for the possibility of hole doping, the calculations were repeated for 0.1 and 0.2 holes per Ni atom. The results are shown in Supplementary Figs. 13 and 14. The discussed trends are similar for all doping. In addition, we computed the quasiparticle contribution to the longitudinal, transverse conductivities, including the individual band contributions and the total Hall coefficient at T = 60 K using the previously developed Kubo formalism for correlated electrons and the results are shown in Supplementary Fig. 12.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Dear Authors,\nIn this manuscript, the authors report on the effect of pressure on the superconductivity in bilayer nickelate thin films. This\nstudy is an important and timely exploration of the connection between the differences between superconductivity in bulk\nmaterials under pressure and it in compressively-strained thin films at ambient pressure. I agree that the sentence in\ndiscussion page 17 line 356 [The combination of strain engineering and high pressure is an essential tool in the research of\nnickelate superconducting thin films.] While the authors measured four samples under applied pressure, the results are quite\ncomplicated. The authors could improve the presentation of the data to make it easier to understand. Theoretical\ncalculations provide some insight, but the discussion in this manuscript seems not sufficient to explain the complicated\nresults.\nTo convince the general reader of the claims in this manuscript, it would be better to make major revisions to improve the\npaper, such as the addition of figures.\n1, The definition of the onset superconducting transition temperature should be reconsidered. The definition applied in Fig.\n1a in ref. 40, Y. Liu et al., Nature Materials 24, 1221 (2025). is most reliable and common method. Thie method should be\napplied to estimate the onset transition temperature. This method is also applied in Fig. 1 in ref. 13. To resolve the confusion\nregarding the transition temperature of bilayer nickelate thin films, it is appropriate to apply a reliable definition. In particular,\nthe temperature values of broad transitions for Fig. 2b, Fig. 3b, suppl. Fig. S1, and Fig. S7b in this manuscript are strongly\naffected by how to be defined. For example, linear approximation in the transition region can be defined as the range\nbetween 80% and 90% of normal resistance values. By adopting this method, it is possible to compare all data through fair\nanalysis. The experimental observation of the enhancement under applied pressure itself is a main claim of this manuscript.\nThe temperature values should be compared by fair definition.\nTo remove the confusion by the different definition between this manuscript and previous studies ref. 40 and ref. 13, the\nauthors should revise the definition with applying identical method.\n2, There is no consistent explanation for the strange behaviour that the transition temperature increases with increasing the\nresistivity. This observation may come from the artifact by applying inadequate definition method discussed in comment 1.\nWhile the increase of the transition temperature may be induced by increase of Fermi surface or other enhancement of\ninteraction, the increase of the resistance likely comes from the reduction of charge carrier density and/or increase of\nscattering. If these phenomena occurs simultaneously in the sample, how did the authors explain consistently for both the\nincrease of transition temperature and resistance? These phenomena are independently discussed in the present\nmanuscript, but the consistent explanation is necessary to convince the claim to readers.\n3, The resistance values at 300 K for four samples in this study should be compared by plotting as a function of pressure to\nmake clear the reproducibility of the pressure effect. Whether superconductivity occurs or not is an important point, but it is\nalso important to compare the reproducibility in the resistivity of the normal state before that occurs. It is expected that the\nresistance variation by applying pressure should systematically occur via shorten lattice and increase of Fermi surface. If the\nauthors claim the reproducibility, this point should be clearly explained with additional data plots.\n4, In addition to the comment 2, can the simultaneous occurrence of increase of resistance and transition to the insulator be\ninterpreted by theoretical band calculation ? These behaviours were not observed in bulk studies. This point may not be\nexplained in the present manuscript. While four samples in this study show similar behaviour, the difference between bulk\nresults under pressure and that in this study should be discussed.\nIntuitively, the applying pressure shrinks the lattice, corresponding to the increase of Fermi surface and in-plane hopping. It\nis likely that the resistance value decreases with increasing pressure up to a certain critical pressure condition, for example\noccurrence of structural phase transition. If such transition occurs in bilayer nickelate film, which will be also observed in\nbulk.\n5, In this study, four samples were measured and discussed under pressure. In Fig. 1d, the resistivity values of six films are\nplotted. But in other figures under pressure, the resistance values are plotted. Were the resistance results, resistivity and\nresistance, consistent and reproducible? Judging from the high values of resistivities, the highest S6, S4, S2+35 days, S2,\nS5, S3, S1+35 days, and the lowest S1are plotted. S6 and S1 is the highest and lowest, respectively. However, the values\nfor 600 Ohm of S3 in Fig. 3, 300 Ohm of S4 in Fig. S7, 200 Ohm of S1 in Fig. 2, and 150 Ohm of S2 in Fig. S3 are not\nconsistent to the resistivities shown in Fig. 1. If this difference comes from the sample geometry, the authors should present\nthe photo of all samples or its summary in tables to explain the geometrical difference. If the sample size and geometry are\ncomparable, the authors have to explain the origin for this inconsistent resistivity / resistance shown in the Figures.\n6, Is the comparison with infinite layer nickelate meaningful? In page 3 line 49, the authors describe that [This is strongly\ncontrasted to the 3d^9 configuration in cuprates and infinite-layer nickelates.]. Why do the authors compare their results\nunder pressure with infinite layers when they believe that the electronic structure and the origin of superconductivity are\nclearly different?\n7, in page7, line 150, what does the reference 1 and 14 mean? Refs 1 and 14 correspond to bulk studies. In addition, in\npage 6 line 116-117, 20.75 A is elongated. The authors should describe the bulk value of c-axis length at ambient pressure.\nWhat does [abnormal elongation] mean? The comparison with the c-axis in previous film studies may be meaningful.\n8, in page 9 line 193, [The slight increase of RH above 2.2 GPa may be induced by the solidification of PTM. Such behavior\nindicates that the carrier concentration increases upon applying a pressure.] These explanations seem too simplified. How\ndoes the solidification of PTM affect the RH of the film? Is this behavior observed in other materials by applying identical\nPTM? Moreover, as described in page 6 line 135, the RH of the bilayer nickelates is more complicated due to the multiband\nnature of the electronic structure of bilayer nickelates. The increase of RH does not simply indicate the increase of carrier\nconcentration. The authors should provide a unified explanation throughout the text.\n9, in page 10 line 208, honestly speaking, it is rather difficult to agree that the description [Although the temperature\ndependence of normal-state resistance exhibits a drastic evolution, the superconducting onset transition temperature\ndependence shows a clear enhancement at relative low pressures.] because the shift of transition is small in Fig. 3a.\nMoreover, the description in line 216-217 [the R(T) curves display nearly similar evolutions as sample S3 under high\npressures, which first shows a decrease from 2 to 4 GPa and then increases gradually with further increasing pressure.] is\nnot fair. The authors have to be fair. For sample S3, the resistance firstly increases from 0 GPa to 2 GPa. Why did the\nauthors only explain the behavior from 2 to 4 GPa not from 0 to 2 GPa?\n10, What does this description [As is known, the delicate nickelate thin films can be easily and partially deteriorated at high\npressures when the liquid PTM solidifies, which would produce disorders and defects in the thin film that will enhance the\ncarrier scattering.] mean? Probably, no one knows that the bilayer nickelate film is easily deteriorated by applying pressure\nbecause there are less studies. Many bulk crystals show reproducible results under pressure. In addition, in ref. 54, there is\nno similar deterioration. If the authors would like to conclude that the films in this study are easily deteriorated, this would\nsuggest that they were inferior specimens with insufficient crystal quality to withstand the pressure application experiments.\nThe authors may need to reconsider the pressure effect once the quality of thin film samples reaches a level comparable to\nthat of bulk crystals.\nAlternatively, the authors should clearly describe the upper limit of pressure at which the intrinsic property of the nickelate\nfilms can be discussed in this study. To remove the confusion to general readers, it would be better that the authors describe\nthe observed results above the upper limit come from the extrinsic effect or PTM effect.\n11, in page 13 line 277, how does the solidification affect the electronic structure of the film?\n12, in page 13 line 288, only c-axis length is defined. How is the a-axis length defined in the calculation model? If the\nauthors discuss the pressure effect, the a-axis should be also compressed as increasing pressure.\n13, in page 14 line 303, Fig. 5d is firstly explained in main text. To improve the readability, it would be better that the authors\neither change the order of the figures or change the order of the explanations in the text.\n14, in page 17 line 360-371, it is difficult to agree that the discussion in this study. Are the claims in this discussion firstly\nfound in this manuscript? Because no reference is added, it would be better to check this point again. Moreover, it would be\nbetter to discuss here the consistency between film and bulk. If the interplay between interlayer and intralayer electronic\ncorrelation induces the reduction of the transition temperature, why this reduction has not been observed in bulk under\npressure?\n15, in page 18, line 389, although the transition temperature in ref. 54 seems similar, the overall behaviour under pressure\nseems completely different, no insulating behaviour appear in ref. 54. What is the origin of this difference?\n16, in page 20 line 424, a five-probe method is described. The sample photo should be provided to explain the\nmeasurement configuration. Was the current uniformly applied to the small (0.6 mm x 0.3 mm) sample with five electrodes ?\n17, It would be better to reconsider the offset for the resistance data shown in Fig. 3b and Fig. S7, because the minus value\nof resistance seems strange. Moreover, the offset value should be explicitly explained if it is added to the data. In general,\nthe equal offset is added to the data.\n18, It would be better to reconsider the color of the data shown in Fig. 1d, Fig. 3, and Fig. S7. It is difficult to recognize the\ncorrespondence of data.\n19, in page 11 line 244, it is difficult to agree with [relatively sharp] for the data of 13 GPa. If the authors quantitatively discuss\nthe sharpness of transition, it would be helpful to understand the evaluation standard.\n20, the bilayer heterostructure La2.5Pr0.5Ni2O7 / La2.85Sr0.15Ni2O7 is applied to this pressure study. The basic resistance\nresults of single films of 3 unit-cell La2.5Pr0.5Ni2O7 and 3unit-cell La2.85Sr0.15Ni2O7 are quite helpful to understand the\neffectiveness of the bilayer heterostructure. It would be better to present those results in supplement.", "reviewer_2": "This is an excellent manuscript with a significant contribution to the field of high-temperature superconductivity in nickelates\nLa3Ni2O7. The authors successfully demonstrate a pressure-induced enhancement of superconductivity in compressively\nstrained thin film samples, revealing a dome-shaped T-P phase diagram. The combination of high-quality experimental data\nand insightful theoretical analysis provides a compelling case for the proposed mechanism. I believe this work is highly\nsuitable for publication and recommend its acceptance following a thorough and careful revision based on the following\ncomments.\n(1). The observation of a transition from metallic to weak insulating behavior at pressures above the optimal 9 GPa is a\ncritical and intriguing finding. To fully substantiate this phenomenon and provide deeper insight, a more detailed analysis is\nrequired. It would be invaluable to see the full resistance-temperature curves at pressures both below and above this\ntransition point. A discussion on whether this behavior is linked to an intrinsic structural or electronic phase transition, such\nas a charge density wave or Fermi surface reconstruction, would be highly valuable. Are there any other signatures or\ncharacteristics of this weak insulating behavior (e.g., a change in the resistance slope, hysteretic behavior, or\nmagnetoresistance behavior) that could provide additional insights? Providing a more detailed picture of the normal state\nproperties in this high-pressure regime will greatly strengthen the manuscript's conclusions.\n(2). The manuscript attributes the enhanced superconductivity to a synergy of enhanced orbital hybridization, improved\nitinerancy, and stronger magnetic fluctuations. While the qualitative argument is sound, a more quantitative or at least\nqualitative analysis distinguishing the relative importance of these factors would be a significant addition. Furthermore, given\nthe discussion of magnetic fluctuations as the likely pairing glue, a brief discussion on the likely symmetry of the\nsuperconducting pairing (e.g., d-wave or s-wave) and how it evolves under pressure, or a future outlook on this topic, would be\nhighly beneficial for a comprehensive understanding.\n(3). The theoretical model assumes that applied hydrostatic pressure primarily reduces the out-of-plane lattice constant, with\nthe in-plane constant clamped by the substrate.\nHowever, smaller in-plane lattice constant would also influence the electronic behavior, e.g., leading to enhanced intralayer\ninterorbital hybridization. Could the authors provide a quantitative estimate of the actual strain state of the film under\npressure? A more detailed justification for the assumption of a fixed in-plane lattice parameter would strengthen the\nconnection between the theoretical model and experimental conditions.\n(4). The Hall effect measurements indicate that the primary charge carriers are holes and that their density slightly increases\nwith pressure. To substantiate this claim, it would be highly beneficial to include specific numerical data or estimations of the\ncarrier concentration at various pressures. Additionally, the manuscript would be significantly enhanced by a qualitative\ndiscussion on how the theoretically predicted alpha, beta, and gamma bands, which are believed to cross the Fermi level,\nevolve under pressure. Specifically, which of these bands is most responsible for the observed hole-like nature of the\ncarriers, and what is its role in contributing to superconductivity? This discussion would offer deeper insights into the\nmicroscopic electronic structure.\n(5). The manuscript could benefit from a brief discussion on the potential influence of the interlayer Ni-O-Ni bond angle, as\nthis factor has been shown to be crucial in other nickelate studies and may be relevant to the observed interlayer spin\nfluctuations.\n(6). There are minor inconsistencies between some figures and the main text. For example, the peak of the superconducting\ndome in Figure 4 (nearly 7.5 GPa) appears slightly different from the value stated (9 GPa) in the text. While the regime\nplotting in Figure 4 is only approximate, it will still be helpful to make the phase diagram more consistent with the text.", "reviewer_3": "Li et al. presents a comprehensive investigation of enhanced superconductivity in compressively strained bilayer nickelate\nthin films under hydrostatic pressure. The authors demonstrate that the superconducting transition temperature can be\nenhanced from ~40 K at ambient pressure to over 61.5 K at 9 GPa, revealing a dome-shaped pressure-temperature phase\ndiagram. The study combines experimental work with theoretical calculations to provide insights into the underlying\nmechanisms. Overall, the study addresses an important topic in the rapidly evolving field of nickelate superconductivity and\nthe results are generally well presented.\nI recommend this manuscript for publication in Nature Communications after addressing the following questions and\nsuggestions:\n1. Heterostructure design rationale: The authors employ a heterostructure design with 1.5 UC of La2.5Pr0.5Ni2O7 and 1.5\nUC of La2.85Sr0.15Ni2O7 to enhance stability, but the specific choice of Sr doping concentration (x=0.15) and layer\nthicknesses appears somewhat arbitrary. Could the authors provide more detailed justification for these parameters? Were\nsystematic studies conducted to optimize these values, or were they based on prior literature? Please provide more\ninformation.\n2. Strain characterization limitations: While the authors claim compressive strain based on c-axis elongation from XRD 2θ-ω\nscans, this characterization is insufficient for a heterostructure containing two different compositions with potentially different\nlattice parameters. Reciprocal space mapping (RSM) or transmission electron microscopy (TEM) would provide more\ndefinitive evidence of the strain state and film quality. The current XRD data quality also appears limited for making strong\nclaims about crystalline quality.\n3. Hall coefficient interpretation: The positive Hall coefficients observed in this work contrast with recent literature reports\nshowing negative Hall coefficients in Sr-doped bilayer nickelate films. Given that this heterostructure contains both Sr and\nPr, could the authors provide a more detailed discussion of the charge carrier behaviour and how it relates to the\nsuperconducting mechanism in their specific system?\n4. Data presentation: The resistance vs. temperature data should be converted to resistivity vs. temperature for proper\nmaterials characterization and cross-comparison with others’ work. Additionally, experimental uncertainties should be\nincluded, particularly for the transition temperatures in the phase diagram.\n5. Mechanisms: The manuscript describes two different trends in superconducting transition behaviour under pressure but\ndoes not clearly explain their origins. Could the authors elaborate on what physical mechanisms drive these different\nbehaviours and how they relate to the theoretical calculations?\n6. Reproducibility: While multiple samples are measured, it would be valuable to include a more quantitative discussion of\nsample-to-sample variation in superconducting properties at ambient pressure, particularly given the complexity of the\nheterostructure growth and post-annealing process.\nDespite these questions, this work represents a significant contribution to understanding pressure effects in nickelate\nsuperconductors and successfully demonstrates substantial enhancement of transition temperatures through the\ncombination of strain engineering and pressure tuning.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "Responses to the Reviewers’ report\n(The words in black color are from the reviewers´ reports, and the blue words\ngive our responses)\n--------------------------------------------------------\nResponses to the Report of Reviewer #1\n--------------------------------------------------------\nIn this manuscript, the authors report on the effect of pressure on the\nsuperconductivity in bilayer nickelate thin films. This study is an important and\ntimely exploration of the connection between the differences between\nsuperconductivity in bulk materials under pressure and it in compressively-\nstrained thin films at ambient pressure. I agree that the sentence in\ndiscussion page 17 line 356 [The combination of strain engineering and high pressure is\nan essential tool in the research of nickelate superconducting thin films.] While\nthe authors measured four samples under applied pressure, the results are\nquite complicated. The authors could improve the presentation of the data to\nmake it easier to understand. Theoretical calculations provide some insight, but\nthe discussion in this manuscript seems not sufficient to explain the complicated\nresults.\nTo convince the general reader of the claims in this manuscript, it would be\nbetter to make major revisions to improve the paper, such as the addition of\nfigures.\nResponse: We thank this reviewer for the careful reading and constructive\nsuggestions. The reviewer provided several constructive suggestions, and we\nhave modified our manuscript according to these suggestions/questions. We\nhave made sufficient revisions to the manuscript, for example, we have\nmodified Figs. 1-5 and Supplementary Figs. 3, 5, 7; we have added\nSupplementary Note 1 and 2, Supplementary Figs. 1a, 8, 9, 11 and many new\ndescriptions and discussions. We hope this reviewer will be satisfied with our\nresponses and revisions.\n1. The definition of the onset superconducting transition temperature should be\nreconsidered. The definition applied in Fig. 1a in ref. 40, Y. Liu et al., Nature\nMaterials 24, 1221 (2025). is most reliable and common method. This method\nshould be applied to estimate the onset transition temperature. This method is\nalso applied in Fig. 1 in ref. 13. To resolve the confusion regarding the transition\ntemperature of bilayer nickelate thin films, it is appropriate to apply a reliable\ndefinition. In particular, the temperature values of broad transitions for Fig. 2b,\nFig. 3b, suppl. Fig. S1, and Fig. S7b in this manuscript are strongly affected by\nhow to be defined. For example, linear approximation in the transition region\ncan be defined as the range between 80% and 90% of normal resistance values.\nBy adopting this method, it is possible to compare all data through fair analysis.\nThe experimental observation of the enhancement under applied pressure itself\nis a main claim of this manuscript. The temperature values should be compared\nby fair definition.\nTo remove the confusion by the different definition between this manuscript and\nprevious studies ref. 40 and ref. 13, the authors should revise the definition with\napplying identical method.\nResponse: We thank this reviewer for the constructive suggestion. We agree\nwith the reviewer that the definition of T used in ref. 13 and 40 is good and is\nc\nalso one of the standard methods to define T . The standard “cross-point”\nc\nmethod in the literatures is more suitable for superconductors with sharp\nsuperconducting transitions. In our present data, the superconducting transition\nwidth are relatively wide, and there is even no complete superconducting\ntransition under higher pressure in CAC measurements. Therefore, we follow\nthe suggestion of this reviewer, and define the linear approximation of the\ntransition region by using the data between 80% and 90% of normal resistance\nvalues, and the T cross is defined as the cross-point of this transition region and\nc\nnormal state linear extrapolation (see revised Fig. 2b, Fig. 3b and\nSupplementary Fig. 8). Then, we successfully get a new set of T cross values\nc\nwith pressure dependence of S1 and S3, as shown in the revised Fig. 4.\nAlthough the values are lower than the T onset in our initial manuscript, it seems\nc\nthat the pressure dependence of T cross exhibits similar behavior as T onset under\nc c\npressure. In the revised version, we keep the two sets of data, namely T onset\nc\nand T cross in the phase diagram for the readers to have a better judgement.\nc\nIn the revised manuscript, we have revised Fig. 2b, Fig. 3b and added a new\nSupplementary Fig. 8 to illustrate the definition of T cross and T onset, despite the\nc c\nT cross values are a bit lower in the revised phase diagram. We also made some\nc\nnecessary discussions for why we use both definitions to get T . We hope this\nc\nreviewer is satisfied with our responses and related reversions to the\nmanuscript.\n2. There is no consistent explanation for the strange behaviour that the\ntransition temperature increases with increasing the resistivity. This observation\nmay come from the artifact by applying inadequate definition method discussed\nin comment 1.\nWhile the increase of the transition temperature may be induced by increase of\nFermi surface or other enhancement of interaction, the increase of the\nresistance likely comes from the reduction of charge carrier density and/or\nincrease of scattering. If these phenomena occurs simultaneously in the sample,\nhow did the authors explain consistently for both the increase of transition\ntemperature and resistance? These phenomena are independently discussed\nin the present manuscript, but the consistent explanation is necessary to\nconvince the claim to readers.\nResponse: We thank this reviewer for the careful review. We agree with the\nreviewer that the increase of T may be induced by increase of Fermi surface\nc\nor the enhancement of some interactions. The better metallicity in the normal\nstate in low pressure region (see Fig. 2a) may be induced by the enhanced\nitinerancy of the charge carriers. However, we want to point out that the\nabnormal increase of room temperature resistance (R ) may not reflect the\nintrinsic properties of the bilayer thin films under high pressure. For instance,\nas shown in Fig. S7, the pressure for the abnormal increase of resistivity (~4\nGPa) is much lower than the pressure for the saturation of T (~8 GPa).\nc\nTherefore, we may attribute the increase of normal state resistance to the\ndamage to the electric connection of the film caused by the solidification of the\npressure-transmitting medium. The reasons are as follows: (1) For different\nruns of experiment (S3 in Fig. 3 and S4 in Fig. S7) on our bilayer thin films, the\nevolution of superconducting transition temperature with pressure is relatively\nconsistent with each other, while the critical pressure for the increase in normal\nstate resistance is quite different. (2) Similar increase of normal state resistance\nunder high pressure were also observed in the infinite layer thin film [see the\ndata in ref. 46: Wang, N. N. et al., Nat. Commun. 13, 4367 (2022)]. However,\nthe T in 112 thin films is monotonically increased without saturation, which may\nc\nindicate that there is no correlation between the change in T and absolute\nc\nvalue of normal state resistance in thin films for the high-pressure measurement\nin CAC apparatus. Therefore, we believe that the abnormal increase of\nresistance in our thin films under pressure are most likely due to the extrinsic\nreasons. To address these issues more clearly for the readers, we have added\nsome necessary explanations in the main text and a new Supplementary Note\n2 in the revised Supplementary Information to discuss the possible reason for\nthe abnormal enhancement of resistance in our high-pressure measurement.\n3. The resistance values at 300 K for four samples in this study should be\ncompared by plotting as a function of pressure to make clear the reproducibility\nof the pressure effect. Whether superconductivity occurs or not is an important\npoint, but it is also important to compare the reproducibility in the resistivity of\nthe normal state before that occurs. It is expected that the resistance variation\nby applying pressure should systematically occur via shorten lattice and\nincrease of Fermi surface. If the authors claim the reproducibility, this point\nshould be clearly explained with additional data plots.\nResponse: As we responded to the reviewer for comment 2, the abnormal\nincrease of resistance values at room temperature (R ) may not reflect the\nintrinsic properties of our thin films under pressure. As shown in Fig. R1 below,\nwe plot the pressure dependent room-temperature resistivity (ρ ) of the four\nthin films. It can be clearly seen that in low-pressure region, the room\ntemperature resistivity decreases continuously and shows good reproducibility\nwith each other, indicating a possible consequence of the shorten lattice\nconstant and increase of Fermi surface of our samples under pressures as\npointed out by the reviewer in this comment. However, in the high-pressure\nregion, it shows an opposite behavior, we don`t have the intention to attribute\nthe abnormal increase of resistivity with pressure to the intrinsic pressure effect\nof the bilayer thin films. There are several extrinsic factors that can affect the\nabsolute resistivity of thin films when pressure is high. For example, the change\nof the pressure environment, the variation of the electrode contact, defects or\ndisorders generated by pressure, etc. For our samples with different PTM (S3\nand S4) and different samples with the same PTM (our samples and 112 thin\nfilms in ref. 46), the abnormal change of resistivity always occurs and the critical\npressure for this phenomenon seems to be quite random. Therefore, in order\nto clarify this issue, we add a new Supplementary Note 2 and make necessary\nrevisions to the main text in the revised manuscript.\nWe hope this reviewer will be satisfied with our revised version and the\nexplanations concerning the abnormal change of room temperature resistivity\nunder high-pressures.\nFig. R1: Pressure dependent room-temperature resistivity (ρ ) for different LSP thin\n293K 327\nfilms. The abnormal increase of ρ from 0 to 2 GPa for S4 might be caused by\n293K\nchanges in the electrode contact when applying PTM on samples.\n4. In addition to the comment 2, can the simultaneous occurrence of increase\nof resistance and transition to the insulator be interpreted by theoretical band\ncalculation? These behaviours were not observed in bulk studies. This point\nmay not be explained in the present manuscript. While four samples in this\nstudy show similar behaviour, the difference between bulk results under\npressure and that in this study should be discussed.\nIntuitively, the applying pressure shrinks the lattice, corresponding to the\nincrease of Fermi surface and in-plane hopping. It is likely that the resistance\nvalue decreases with increasing pressure up to a certain critical pressure\ncondition, for example occurrence of structural phase transition. If such\ntransition occurs in bilayer nickelate film, which will be also observed in bulk.\nResponse: We thank this reviewer for the careful review and this comment. As\nwe responded to this reviewer in comments 2 and 3, the increase of resistance\nin the high-pressure region may be due to extrinsic reasons. Some of the\nconduction paths of the thin films may be partially destroyed due to change of\nthe pressure environment, such as the solidification of the PTM, producing\nconsiderable amount of dislocations and defects on the films. Similar behavior\ncan also be seen in the previous work on the infinite-layer nickelates in ref. 46:\nWang, N. N. et al., Nat. Commun. 13, 4367 (2022). For the appearance of weak\ninsulating behavior above T in high pressure region, we can indeed get some\nc\ninformation from theoretical calculation. Our calculations, however, also show\nthat beyond some pressure values the electronic structure changes are minimal,\nreaching some kind of saturation. Therefore, we believe the weak insulating\nbehavior in bilayer thin film may be induced by the gradually enhanced\ncorrelation effect, associated with the shift of the γ-pocket with a flat band\nfeature, which intimately leads to the formation of the density wave order.\nAlthough such insulating behavior is not observed in bulk samples under\npressure, we want to note that, in thin film form of nickelate superconductors,\nthe weak insulating behavior is also observed in Sr-doped La Ni O with dome-\n3 2 7\nlike superconducting region [also see ref.39 and 45]. The different behavior\nbetween thin films and bulk crystals might be attributed to the completely\ndifferent situations within the thin film and the bulk. The pressure induced\nstructural disorders and dislocations may be prominent for these ultra-thin films\nbut is less pronounce on the bulk samples. In bulk crystals, there is no initial\nstrain and the superconductivity is induced by suppressing the weak insulating\nstates and a structural phase transition occurs. However, in thin films, it is\nalready superconductive at ambient pressure and the c-axis lattice constant is\nelongated due to the compressive strain given by substrate. Therefore, the\nelectronic structure may be different from the bulk samples.\nAs for the possibility of structure phase transition, we think there is no direct\nindication for this transition in our films under pressure. Again, we believe that\nthe increase of resistance in high pressures in our experiment is extrinsic,\nand it cannot serve as evidence for a possible structural phase transition.\nIn the revised manuscript, we have modified the related discussions\nregarding to the origin of weak insulating behavior in the point of theoretical\ncalculations. We hope this reviewer will agree with our related revisions and\nchanges to the manuscript.\n5. In this study, four samples were measured and discussed under pressure. In\nFig. 1d, the resistivity values of six films are plotted. But in other figures under\npressure, the resistance values are plotted. Were the resistance results,\nresistivity and resistance, consistent and reproducible? Judging from the high\nvalues of resistivities, the highest S6, S4, S2+35 days, S2, S5, S3, S1+35 days,\nand the lowest S1 are plotted. S6 and S1 is the highest and lowest, respectively.\nHowever, the values for 600 Ohm of S3 in Fig. 3, 300 Ohm of S4 in Fig. S7,\nthe resistivities shown in Fig. 1. If this difference comes from the sample\ngeometry, the authors should present the photo of all samples or its summary\nin tables to explain the geometrical difference. If the sample size and geometry\nare comparable, the authors have to explain the origin for this inconsistent\nresistivity / resistance shown in the Figures.\nResponse: We thank the reviewer for reminding us of this issue. Since the\nspace for high pressure measurement in PCC is much larger than that in CAC,\nthe sample sizes in Fig.2 and Fig. S3 are much larger than that in Fig. 3 and\nFig. S7. That is why the resistance value is bigger in CAC measurement. In the\nrevised manuscript, we have converted the resistance data into resistivity in\nrevised Fig.2(a-c), Fig. 3; Supplementary Fig. 3, Fig. 5, Fig. 7-9 for the\nconsistency of data. We can see that the data present in the revised figures are\nbetter normalized. The little variations for the values of resistivity in Fig .1d and\nthose measured under high pressure is inevitable. The possible reasons are\nlisted as follows: (1) The inhomogeneity of thin films. since we have remade the\nelectrodes during the high-pressure measurements, the slight variation of the\nvalues of resistivity is acceptable if the thin films have some kinds of\ninhomogeneity. (2) The slight degradation of the film. In CAC measurements,\nwe need to greatly reduce the thickness of the substrate by polishing, which\ncould affect the resistivity of the samples. We have added this information to\nthe main text in revised manuscript.\n6. Is the comparison with infinite layer nickelate meaningful? In page 3 line 49,\nthe authors describe that [This is strongly contrasted to the 3d^9 configuration\nin cuprates and infinite-layer nickelates.]. Why do the authors compare their\nresults under pressure with infinite layers when they believe that the electronic\nstructure and the origin of superconductivity are clearly different?\nResponse: We agree with the reviewer on this issue and have no intention to\nhave a comparison with infinite layers. Thus, we have removed the related\nsentence and references in the revised manuscript.\n7. in page7, line 150, what does the reference 1 and 14 mean? Refs 1 and 14\ncorrespond to bulk studies. In addition, in page 6 line 116-117, 20.75 A is\nelongated. The authors should describe the bulk value of c-axis length at\nambient pressure. What does [abnormal elongation] mean? The comparison\nwith the c-axis in previous film studies may be meaningful.\nResponse: We thank the reviewer for these useful suggestions. In the revised\nmanuscript, we have added the c-axis lattice constants of bulk crystals at\nambient pressure and compare the c-axis lattice constant with previous\nreported films. The expression “abnormal elongation” is also revised since it\nwas improperly used in the old version of the main text.\n8. in page 9 line 193, [The slight increase of R above 2.2 GPa may be induced\nH\nby the solidification of PTM. Such behavior indicates that the carrier\nconcentration increases upon applying a pressure.] These explanations seem\ntoo simplified. How does the solidification of PTM affect the R of the film? Is\nH\nthis behavior observed in other materials by applying identical PTM? Moreover,\nas described in page 6 line 135, the R of the bilayer nickelates is more\nH\ncomplicated due to the multiband nature of the electronic structure of bilayer\nnickelates. The increase of R does not simply indicate the increase of carrier\nH\nconcentration. The authors should provide a unified explanation throughout the\ntext.\nResponse: We thank the Reviewer for reminding us of this issue. As we\ndiscussed in the response to comment 2, the solidification of PTM might induce\nlarge number of dislocations or defects in the films, which further affects the\nresistance value of the films. However, this may not have clear effect on the\nHall resistivity since the ρ is only related to the thickness of thin films. In this\nxy\nsense, we agree with the reviewer that the solidification of PTM may not affect\nthe R of the film. Considering the multiband nature of the electronic structure\nH\nof bilayer nickelates, we also agree with the reviewer that the decrease of R\nH\nshould not directly indicate the increase of carrier concentration. In multiband\nsystem, the carrier concentration is also related to the change of carrier mobility\nand the electronic scattering mechanism. Thus, the nonmonotonic change of\nR under pressure in Fig. 2d may be related to the modification of the electronic\nH\nband structure or the multiband contribution of the electron and hole charge\ncarriers.\nIn the revised manuscript, we change the related expressions on the\npressure dependent R and try to give a unified explanation for the R data.\nH H\nWe hope our related reversions can remove the concerns of the reviewer on\nthis issue.\n9. in page 10 line 208, honestly speaking, it is rather difficult to agree that the\ndescription [Although the temperature dependence of normal-state resistance\nexhibits a drastic evolution, the superconducting onset transition temperature\ndependence shows a clear enhancement at relative low pressures.] because the\nshift of transition is small in Fig. 3a. Moreover, the description in line 216-217\n[the R(T) curves display nearly similar evolutions as sample S3 under high\npressures, which first shows a decrease from 2 to 4 GPa and then increases\ngradually with further increasing pressure.] is not fair. The authors have to be\nfair. For sample S3, the resistance firstly increases from 0 GPa to 2 GPa. Why\ndid the authors only explain the behavior from 2 to 4 GPa not from 0 to 2 GPa?\nResponse: We thank this reviewer for the critical reading to the data. As we\ndiscussed above, the change of resistance value under pressures may be\naffected by many extrinsic factors, such as the change of pressure environment\ndue to the solidification of PTM, or the generation of defects in the sample under\npressure, etc. The unusual change in resistivity of S4 from 0 to 4 GPa may be\ndue to the changes in the electrode contact when applying PTM on samples.\nTherefore, because there are too many extrinsic factors that can affect the\nabsolute resistivity of thin films, we cannot reach a reconciled conclusion on the\nnonmonotonic change of the resistance in the present stage.\nAccording to the reviewer`s comments and suggestions, we modified the\ndescriptions in Page 10 line 208 and 216 and also added a new Supplementary\nNote 2 in the revised version to clarify the related issues concerning the\npossible reasons for the nonmonotonic change of resistivity of thin films under\npressure.\n10. What does this description [As is known, the delicate nickelate thin films\ncan be easily and partially deteriorated at high pressures when the liquid PTM\nsolidifies, which would produce disorders and defects in the thin film that will\nenhance the carrier scattering.] mean? Probably, no one knows that the bilayer\nnickelate film is easily deteriorated by applying pressure because there are less\nstudies. Many bulk crystals show reproducible results under pressure. In\naddition, in ref. 54, there is no similar deterioration. If the authors would like to\nconclude that the films in this study are easily deteriorated, this would suggest\nthat they were inferior specimens with insufficient crystal quality to withstand the\npressure application experiments. The authors may need to reconsider the\npressure effect once the quality of thin film samples reaches a level comparable\nto that of bulk crystals.\nAlternatively, the authors should clearly describe the upper limit of pressure at\nwhich the intrinsic property of the nickelate films can be discussed in this study.\nTo remove the confusion to general readers, it would be better that the authors\ndescribe the observed results above the upper limit come from the extrinsic\neffect or PTM effect.\nResponse: We thank this reviewer for the careful review and this comment.\nWe are sorry that the word “deteriorated” was improperly used and we have\nrevised it in our revised version. Under high pressures, some defects or\ndisorders can be introduced in the thin films due to the change of pressure\nenvironment. At high pressures on a very thin film, some micro-cracks,\ndisorders and dislocations may appear, which can naturally cause the\nincrement of resistance. However, these defects, dislocations and even micro-\ncracks might not give strong influence on the electronic structures, and thus the\nappearance of superconductivity.\nAs we clearly discussed in the new Supplementary Note 2 of the revised\nmanuscript, the PTM induced disorders can only affect the values of resistance\nas it may disrupt the conducting channels in certain areas of the thin films.\nHowever, the temperature dependence of resistance and the superconducting\ntransition temperature should not be affected, and these properties always\nreflect the intrinsic behavior of our bilayer thin films in the whole pressure range\nwe measured. Therefore, the evolution of T s and weak insulating behavior\nc\nunder pressure seem to be true and repeatable experimental results.\n11. in page 13 line 277, how does the solidification affect the electronic structure\nof the film?\nResponse: Thanks for the question. We think the solidification of PTM will not\naffect the electronic structure of the film. It merely introduces defects and micro-\ncracks on the film surface, thereby affecting the normal state resistance.\nTherefore, we didn`t discuss this issue in our original manuscript. However, we\nadded one sentence in the revised version to stress on this issue.\n12. in page 13 line 288, only c-axis length is defined. How is the a-axis length\ndefined in the calculation model? If the authors discuss the pressure effect,\nthe a-axis should be also compressed as increasing pressure.\nResponse: We thank the reviewer for pointing out this issue. For our bilayer\nnickelate films we emulate applied pressure by compressing the out-of-plane\nlattice parameter c while keeping the in-plane lattice constant a fixed at its\nambient pressure value. This choice reflects the experimental geometry: the\nfilm is epitaxially clamped to a rigid substrate so the in-plane lattice is set by the\nsubstrate (and is not free to relax under moderate external pressure), while the\nfilm is free to change its interlayer spacing. Physically, the dominant pressure-\ndriven changes in the electronic structure of layered nickelates arise from\nmodifications of interlayer coupling, apical-oxygen distances, and Ni-O bond\nangles — all of which are controlled primarily by c and by internal atomic\nrelaxations. Computationally, fixing a while fully relaxing internal coordinates for\neach c gives the correct symmetry and the principal microscopic degrees of\nfreedom affected by pressure, and it also allows straightforward comparison to\nfilm experiments where in-plane clamping is present.\n13. in page 14 line 303, Fig. 5d is firstly explained in main text. To improve the\nreadability, it would be better that the authors either change the order of the\nfigures or change the order of the explanations in the text.\nResponse: We thank the Referee for this comment, and followed his/her\nrecommendation, Fig. 5 is updated accordingly. We hope this reviewer will\nagree with the revised version.\n14. in page 17 line 360-371, it is difficult to agree that the discussion in this\nstudy. Are the claims in this discussion firstly found in this manuscript?\nBecause no reference is added, it would be better to check this point again.\nMoreover, it would be better to discuss here the consistency between film and\nbulk. If the interplay between interlayer and intralayer electronic correlation\ninduces the reduction of the transition temperature, why this reduction has not\nbeen observed in bulk under pressure?\nResponse: We thank the Reviewer for the comment. Certainly, the referee is\nright that our formulation was very general and many relevant points were\ndiscussed by multiple groups, which we also cited throughout the manuscript.\nThus, we have modified now this paragraph by explicitly mentioning difference\nbetween the thin films and the bulk. In particular, in strained thin films, external\npressure acts on a lattice already clamped by the substrate, so the in-plane\nlattice constants and the in-plane Ni-O-Ni bond angle remain largely fixed while\ncompression is mostly accommodated along the out-of-plane direction. On the\ncontrary, in the bulk crystals there is a remarkable correspondence between the\nin-plane Ni-O-Ni bond angle and the T value once the structural transition to\nc\nthe I4/mmm phase takes place, see for example Fig.1 in B. Samanta, and A.B.\nGeorgescu, arXiv: 2506.11427. Note, in compressed thin films the in-plane\nbond Ni-O angle is more bent than those achieved under hydrostatic pressure,\ncorrelating with a lower T . Thus, our hypothesis is that in thin films pressure\nc\nmostly affects the c-lattice constant, while keeping in-plane Ni-O-Ni bond angle\nfixed. Thus, the effect of the hydrostatic pressure on the bulk and thin films is\nlargely different.\nIndeed, the reduction of transition temperature in bulk crystals under high\npressure were observed. In ref. 1 and 21, the reported T value always\nc\ndecreases with increasing pressure in bulk bilayer nickelate samples. As we\nmentioned above, the pressurizing effect on the lattice constants in thin films\nare very different from the bulk samples, thus the T dependence of the thin\nc\nfilms and bulk samples should have some differences. In the revised Discussion\nsection, we have re-formulated the corresponding sentences in the conclusion.\n15. in page 18, line 389, although the transition temperature in ref. 54 seems\nsimilar, the overall behaviour under pressure seems completely different, no\ninsulating behaviour appear in ref. 54. What is the origin of this difference?\nResponse: We thank the reviewer for the careful review and this comment. We\nthink the origin of the difference between our data and that in ref. 54 (ref. 55 in\nthe revised version) is because of the different strains applied on thin films.\nThis will induce significant difference of electronic band structures and transport\nproperties. In ref. 54, the films are grown on substates with tensile strains\n(SrTiO : +1.9%; NdGaO : +0.6%) or slightly compressive strains (LaAlO : -\n3 3 3\n0.5%) comparing to our present study (SrLaAlO : -2%). The ground states of\n3 2 7\nwhile our film has already become superconducting at ambient pressure.\nTherefore, the different behavior of our films and that in ref. 54 under high\npressure are understandable. We believe that by applying higher pressure to\nthe thin films in ref.54, the behavior of weak insulation above T might also occur.\nc\n16. in page 20 line 424, a five-probe method is described. The sample photo\nshould be provided to explain the measurement configuration. Was the current\nuniformly applied to the small (0.6 mm x 0.3 mm) sample with five electrodes?\nResponse: We thank this reviewer for the suggestion. We have provided the\nsample photo showing standard five-probe electrode configuration as an inset\nin the revised Fig. 1c. The Hall coefficient measurements are done in the\npiston–cylinder cell, where the sample size is much bigger than that used in\nCAC. The typical size for our measurement is 3 mm x 1.5 mm, and the current\nis supposed to be uniformly applied on the thin films. In the revised version,\nwe have added the sample photo and necessary explanation for the Hall\nmeasurement.\n17. It would be better to reconsider the offset for the resistance data shown in\nFig. 3b and Fig. S7, because the minus value of resistance seems strange.\nMoreover, the offset value should be explicitly explained if it is added to the data.\nIn general, the equal offset is added to the data.\nResponse: We thank the reviewer for this comment. According to this\nsuggestion, we have replotted the Fig. 3b and Fig. S7 to avoid the minus value\nof resistance in the revised manuscript. In order to prevent the curves from\nintersecting with each other and thereby affecting the visualization of the\nsuperconducting transition, we made necessary vertical shifts to the curves\nexcept for the 0 GPa one. The offset of the curves under high pressure is non-\nequal in each increment.\n18. It would be better to reconsider the color of the data shown in Fig. 1d, Fig.\n3, and Fig. S7. It is difficult to recognize the correspondence of data.\nResponse: We agree with the reviewer for this suggestion. In the revised\nversion, we have changed the colors in Fig. 1d, Fig. 3 and Fig. S7. We think the\nnew colors are much easier to distinguish from each other. We hope the\nreviewer is satisfied with these modifications.\n19. in page 11 line 244, it is difficult to agree with [relatively sharp] for the data\nof 13 GPa. If the authors quantitatively discuss the sharpness of transition, it\nwould be helpful to understand the evaluation standard.\nResponse: We thank the reviewer for the careful review. Due to the pressure\ninduced weak insulating behavior and lose of zero resistance state under high\npressures in Fig. 3, it is difficult to quantitatively describe the sharpness of the\ntransition. In our present study, we focus more on the onset transition\ntemperature rather than the sharpness of the transition itself. Therefore, we\nagree with this reviewer that it is inappropriate to say the superconducting\ntransition is relatively sharp in Fig.3. We think a more accurate description\nwould be: “a clear resistance drop”. In the revised manuscript, we have carefully\nchecked the descriptions concerning the superconducting transitions and make\nsome necessary reversions.\n20. the bilayer heterostructure La Pr Ni O /La Sr Ni O is applied to this\n2.5 0.5 2 7 2.85 0.15 2 7\npressure study. The basic resistance results of single films of 3 unit-cell\nLa Pr Ni O and 3unit-cell La Sr Ni O are quite helpful to understand\n2.5 0.5 2 7 2.85 0.15 2 7\nthe effectiveness of the bilayer heterostructure. It would be better to present\nthose results in supplement.\nResponse: We thank the reviewer for the suggestion. As we addressed in our\nmanuscript, the bilayer heterostructure La Pr Ni O /La Sr Ni O are\n2.5 0.5 2 7 2.85 0.15 2 7\npretty stable in air conditions, which enables us to conduct subsequent\ninvestigation on the transport properties of the bilayer nickelate thin films under\npressure in different labs with different high-pressure cells. Indeed, we also\nfabricated the pure 3-UC La Sr Ni O and La PrNi O thin films and other\n2.85 0.15 2 7 2 2 7\nheterostructures using the similar growth process, the R(T) curves are shown\nin Fig. R2. We can see that the superconducting transition is absent in those Sr\ndoped sample and heterostructures, and La PrNi O are pretty easy to\n2 2 7\ndeteriorate in air. Therefore, we cannot measure the high-pressure resistance\non these samples at present stage.\nFig. R2: a, The normalized ρ (T) curves of pure La Sr Ni O and other\n2.85 0.15 2 7\nheterostructures. b, The normalized ρ (T) curves of La PrNi O and after 10 days.\n2 2 7\nWe would like to thank this reviewer for the careful review and the constructive\ncomments/suggestions. With the point-to-point responses and related revisions,\nwe hope this reviewer will make a positive recommendation to our work for\npublication.\n--------------------------------------------------------\nResponses to the Report of Reviewer #2\n--------------------------------------------------------\nThis is an excellent manuscript with a significant contribution to the field of high-\ntemperature superconductivity in nickelates La Ni O . The authors successfully\n3 2 7\ndemonstrate a pressure-induced enhancement of superconductivity in\ncompressively strained thin film samples, revealing a dome-shaped T-P phase\ndiagram. The combination of high-quality experimental data and insightful\ntheoretical analysis provides a compelling case for the proposed mechanism. I\nbelieve this work is highly suitable for publication and recommend its\nacceptance following a thorough and careful revision based on the following\ncomments.\nResponse: We appreciate the careful review and positive remarks to our\nmanuscript by this reviewer. We have revised the manuscript according to\nhis/her constructive comments and suggestions as listed below. The revised\nmanuscript is greatly improved according to these suggestions, and we hope\nthe reviewer will be satisfied with the revised version.\n1. The observation of a transition from metallic to weak insulating behavior at\npressures above the optimal 9 GPa is a critical and intriguing finding. To fully\nsubstantiate this phenomenon and provide deeper insight, a more detailed\nanalysis is required. It would be invaluable to see the full resistance-\ntemperature curves at pressures both below and above this transition point. A\ndiscussion on whether this behavior is linked to an intrinsic structural or\nelectronic phase transition, such as a charge density wave or Fermi surface\nreconstruction, would be highly valuable. Are there any other signatures or\ncharacteristics of this weak insulating behavior (e.g., a change in the resistance\nslope, hysteretic behavior, or magnetoresistance behavior) that could provide\nadditional insights? Providing a more detailed picture of the normal state\nproperties in this high-pressure regime will greatly strengthen the manuscript's\nconclusions.\nResponse: This is a very good question. The transition from metallic to weak\ninsulating behavior can be repeatedly observed in different runs of resistive\nmeasurements with the high-pressure CAC apparatus. The full temperature\ndependence of resistance is shown in Fig. 3a, one can see that this transition\nfrom metallic to weak insulating behavior occurs at about 9 GPa. From these\ncurves, the slope of resistance versus T above T can be easily determined. As\nc\nshown in the Fig. R3 below, the slope of the R(T) curves above T in samples\nc\nS3 and S4 changes from positive to negative when entering the weak insulating\nstate after about 9 GPa. We don’t know whether this weak insulating behavior\nis related to the formation of any density wave order, but the phenomena can\nbe easily repeated. We also use a magnetic field to suppress the\nsuperconductivity, the “normal state” recovered by suppressing\nsuperconductivity consistently show the transition from a metallic to a weak\ninsulating behavior and the magnetoresistance in the normal state is negligible\n(see Supplementary Fig. 9d-f in the revised version). The general behavior of\nthe semiconducting part looks like that in underdoped cuprates [R1, R2]. We then\nalso fit the low-T data just above T , indeed a ρ ∝ -lnT relation is found (see\nc\nFig. R4 and Supplementary Fig. S8a-c in the revised version). Thus, we think\nthat the weak insulating behavior may be induced by the gradually enhanced\ncorrelation effect.\nIn addition, as explained in the response to the Reviewer #1, we believe that\nthe observed weakly insulating behavior may be associated an intrinsic density-\nwave (DW) instability, which becomes increasingly relevant at the Fermi level\nunder compression.\nFurthermore, we have performed Hall coefficient calculations within standard\nBoltzmann theory using the obtained electronic structure (see Fig. R5 and also\nSupplementary Fig. 11 in the revised manuscript). In the oxygen-rich (clean)\ncase, the Hall coefficient at ambient pressure is slightly negative, consistent\nwith the results of Ref. [arXiv:2508.15284, Fig. 3]. Upon increasing pressure,\nhowever, the Hall coefficient turns to be positive, reflecting the stronger\ncontribution of the γ-band at the Fermi level. Taken together with the possible\noxygen deficiency present in the films, potential DW instability associated with\nthe movement of γ-band may account for the results we observed\nexperimentally.\nFig. R3: The slope of ρ(T) curves just above T for S3 and S4. We can see that the slope\nc\nchanges from positive to negative at around 9 GPa.\nFig. R4: The ρ versus -lnT curve for S3 at 13 GPa. In the temperature range from 55 to\n[R1] Ando, Y. et al. Logarithmic divergence of both in-plane and out-of-plane normal-state\nresistivities of superconducting La Sr CuO in the zero temperature limit. Phys. Rev. Lett.\n2−x x 4\n75, 4662–4665 (1995).\n[R2] Ono, S. et al. Metal-to-insulator crossover in the low-temperature normal state of\nBi Sr La CuO . Phys. Rev. Lett. 85, 638–641 (2000).\n2 2−x x 6+δ\n2. The manuscript attributes the enhanced superconductivity to a synergy of\nenhanced orbital hybridization, improved itinerancy, and stronger magnetic\nfluctuations. While the qualitative argument is sound, a more quantitative or at\nleast qualitative analysis distinguishing the relative importance of these factors\nwould be a significant addition. Furthermore, given the discussion of magnetic\nfluctuations as the likely pairing glue, a brief discussion on the likely symmetry\nof the superconducting pairing (e.g., d-wave or s-wave) and how it evolves\nunder pressure, or a future outlook on this topic, would be highly beneficial for\na comprehensive understanding.\nResponse: We are thankful to the referee for this comment. The stronger\nhybridization between the Ni-e orbitals can be quantified by the reduced\ng\ncrystal-field splitting as shown in the table below:\nΔ𝑐/𝑐 (in %)\nΔ (in meV) 0\n3𝑑 𝑧2−3𝑑 𝑥2−𝑦2\n451 0\n391 1.5\n316 3.0\n184 5.0\nFurthermore, the data is for the DFT electronic structure and this orbital\nbalancing with pressure is further enhanced with correlations. As a result, there\nis charge flow from Ni-3𝑑 to Ni-3𝑑 orbital, enhancing the presence of\n𝑧2 𝑥2−𝑦2\nthe gamma pocket at the Fermi level. This strengthens the tendency towards\ns+- wave Cooper-pairing. We have added the corresponding sentences in the\nmain text.\n3. The theoretical model assumes that applied hydrostatic pressure primarily\nreduces the out-of-plane lattice constant, with the in-plane constant clamped by\nthe substrate.\nHowever, smaller in-plane lattice constant would also influence the electronic\nbehavior, e.g., leading to enhanced intralayer interorbital hybridization. Could\nthe authors provide a quantitative estimate of the actual strain state of the film\nunder pressure? A more detailed justification for the assumption of a fixed in-\nplane lattice parameter would strengthen the connection between the\ntheoretical model and experimental conditions.\nResponse: This remark is similar to the comment 12 of the Referee #1. As\npointed above, in the bulk crystals there is a remarkable correspondence\nbetween the in-plane Ni-O-Ni bond angle and the T value once the structural\nc\ntransition to the I4/mmm phase takes place, see for example Fig.1 in B.\nSamanta, and A.B. Georgescu, arXiv: 2506.11427. This means that it is the in-\nplane Ni-O-Ni bond angle, which largely controls T in the bulk crystals. In the\nc\nstrained thin films, the situation is different, external pressure acts on a lattice\nalready clamped by the substrate (especially there are only few unit cells in thin\nfilms), so the in-plane lattice constants and the in-plane Ni-O-Ni bond angle\nremain largely fixed (here we refer again to the arXiv:2506.11427), while\ncompression is mostly accommodated along the out-of-plane direction. Along\nthe c-axis, there is the bilayer segment and the LaO spacer segment and\ntherefore much more susceptible to changes with pressure. The smaller, and\nthus \"more homogeneous\", a-axis with the stiff transition metal-O bonds is not\nchanged by pressure in equal terms. The small changes that still happen should\nwork somewhat against the orbital balancing trend described above. Therefore,\nwe assumed the dominant effect from pressure compared to the ambient state\nis driven by the c-axis change. Thus, the effect of the hydrostatic pressure on\nthe bulk and thin films is largely different. We have re-formulated the\ncorresponding sentences in the conclusion.\n4. The Hall effect measurements indicate that the primary charge carriers are\nholes and that their density slightly increases with pressure. To substantiate\nthis claim, it would be highly beneficial to include specific numerical data or\nestimations of the carrier concentration at various pressures. Additionally, the\nmanuscript would be significantly enhanced by a qualitative discussion on how\nthe theoretically predicted alpha, beta, and gamma bands, which are believed\nto cross the Fermi level, evolve under pressure. Specifically, which of these\nbands is most responsible for the observed hole-like nature of the carriers,\nand what is its role in contributing to superconductivity? This discussion would offer\ndeeper insights into the microscopic electronic structure.\nResponse: We thank the reviewer for the suggestion. We followed the\nReferee’s recommendation and present in Fig. R5 the calculated Hall\ncoefficient, modeled within a quasiparticle approximation to the electronic\nstates, as a function of pressure. At ambient pressure, the Hall coefficient is\nsmall and negative, in remarkable agreement with the values reported for\noxygen-rich samples by Maosen Wang et al. (arXiv:2508.15284). With\nincreasing pressure, the Hall coefficient changes sign and becomes positive,\nreflecting the enhanced contribution of the hole-like γ pocket at the Fermi level\nand a stronger tendency toward s± superconductivity.\nExperimentally, however, we consistently observe a positive Hall coefficient.\nBy having a comparison with Ref. 45 [Maosen Wang et al., arXiv:2508.15284],\nthis suggests the presence of a certain degree of oxygen deficiency (interstitials)\nin our samples. Since the α and β bands contribute with opposite signs to the\nHall coefficient and the γ-band contribution is relatively small, oxygen deficiency\nmay dominate the pressure evolution of the Hall response. Consequently, the\nexperimental Hall data should not be interpreted solely as a direct signature of\nelectronic structure evolution under pressure. To achieve a more conclusive\nanalysis, studies on next-generation, higher-quality films will be required.\nFig. R5. Calculated quasiparticle contribution to the longitudinal (left panel),\ntransverse (central panel) conductivities, including the individual band\ncontributions and the total Hall coefficient (right panel) at T = 60 K as a function\nof applied pressure. We employed the Kubo formalism, developed for\nmultiorbital nickelates for the slave-boson renormalized electronic structure, as\ndescribed in ref. R3.\n[R3] S. Bötzel, I.M. Eremin and F. Lechermann, Phys. Rev. B 107, 174526 (2023).\n5. The manuscript could benefit from a brief discussion on the potential\ninfluence of the interlayer Ni-O-Ni bond angle, as this factor has been shown to\nbe crucial in other nickelate studies and may be relevant to the observed\ninterlayer spin fluctuations.\nResponse: We thank this reviewer for raising this interesting point. We agree\nwith the reviewer that the interlayer Ni-O-Ni bond angle is crucial for the\noccurrence of superconductivity in nickelates. However, at this moment, we\ncannot do the synchrotron diffraction measurement on the thin films under\npressure to determine the Ni-O-Ni bond angle. The in-plane lattice is\ndetermined at ambient pressure to be about 3.75 Å, which is about -2% strained\ncompared with the bulk value. The c-axis lattice constant is accordingly\nelongated. Since the thin films are already superconductive at ambient pressure,\nthe Ni-O-Ni bond angle was supposed to be close to 180as the bulk samples\nin the tetragonal phase. Under pressures, we may expect that the Ni-O-Ni bond\nlength will shrink.\nIn theoretical modeling we assume a full tetragonal symmetry of the system.\nNote that the effects of finite Ni-O-Ni bond angle is discussed extensively by B.\nSamanta, and A.B. Georgescu, arXiv: 2506.11427 and we include the reference\nto their paper for consistency.\nIn the revised manuscript, we have some discussion on the interlayer Ni-\nO-Ni bond angle under pressure and its possible relations to the interlayer spin\nfluctuations. We hope the reviewer will satisfied with those reversions and\ndiscussions.\n6. There are minor inconsistencies between some figures and the main text.\nFor example, the peak of the superconducting dome in Figure 4 (nearly 7.5\nGPa) appears slightly different from the value stated (9 GPa) in the text.\nWhile the regime plotting in Figure 4 is only approximate, it will still be helpful to make\nthe phase diagram more consistent with the text.\nResponse: We thank this reviewer for the careful review and this suggestion. In\nthe revised version, we have corrected these inconsistencies.\nWe hope this Reviewer is satisfied with our point-to-point responses and related\nrevisions, and will make a recommendation to our work for publication in Nature\nCommunications.\n--------------------------------------------------------\nResponses to the Report of Reviewer #3\n--------------------------------------------------------\nLi et al. presents a comprehensive investigation of enhanced superconductivity\nin compressively strained bilayer nickelate thin films under hydrostatic pressure.\nThe authors demonstrate that the superconducting transition temperature can\nbe enhanced from ~40 K at ambient pressure to over 61.5 K at 9 GPa, revealing\na dome-shaped pressure-temperature phase diagram. The study combines\nexperimental work with theoretical calculations to provide insights into the\nunderlying mechanisms. Overall, the study addresses an important topic in the\nrapidly evolving field of nickelate superconductivity and the results are generally\nwell presented.\nI recommend this manuscript for publication in Nature Communications after\naddressing the following questions and suggestions:\nResponse: We thank this Reviewer for the careful review and positive remarks\non our work. We also thank the reviewer for the useful and constructive\ncomments/suggestions which have been well addressed in the revised version.\nWe hope the reviewer will be satisfied with our related responses and\nreversions.\n1. Heterostructure design rationale: The authors employ a heterostructure\ndesign with 1.5 UC of La Pr Ni O and 1.5 UC of La Sr Ni O to enhance\n2.5 0.5 2 7 2.85 0.15 2 7\nstability, but the specific choice of Sr doping concentration (x=0.15) and layer\nthicknesses appears somewhat arbitrary. Could the authors provide more\ndetailed justification for these parameters? Were systematic studies conducted\nto optimize these values, or were they based on prior literature? Please provide\nmore information.\nResponse: We thank this reviewer for the careful review and this comment.\nThe heterostructure designed in our present study are quite important for the\ninvestigation of pressure effect on bilayer thin films. We found that with other\nheterostructures, the thin film samples will either lack superconductivity or the\nsuperconductivity will easily deteriorate in air (see the Fig. R6 below). The films\nwith this heterostructure were deposited by using the PLD technique with two\ndifferent targets La Pr Ni O and La Sr Ni O . The deposition and post-\n2.5 0.5 2 7 2.85 0.15 2 7\nannealing conditions have been optimized by having better superconducting\ntransition at ambient pressure (see Supplementary Note 1 in the revised\nversion).\nActually, the values of layer thickness and Sr doping concentration in our\npresent study are mainly based on the previous literatures, and we haven`t\nconducted a systematic study to optimize the thickness and doping\nconcentration yet. We prepared the sample with Sr doping concentration x =\n0.15 because the thin films of La Sr Ni O exhibited the best superconductivity\n3-x x 2 7\naround this doping level (see ref. 39 in the revised version). Furthermore, in ref.\n37 and 39, the superconducting thin films are all fabricated with the thickness\nof 3-UC. Based on this information, we finally decided to grow the bilayer thin\nfilm with a heterostructure of La Pr Ni O /La Sr Ni O with a total\n2.5 0.5 2 7 2.85 0.15 2 7\nthickness of 3-UC in our present study. In the revised manuscript, we have\ngiven some necessary explanations for the choice of Sr doping concentration\nand layer thicknesses.\nFig. R6: a, The normalized ρ (T) curves of pure La Sr Ni O and other\n2.85 0.15 2 7\nheterostructures. b, The normalized ρ (T) curves of La PrNi O and after 10 days.\n2 2 7\n2. Strain characterization limitations: While the authors claim compressive\nstrain based on c-axis elongation from XRD 2θ-ω scans, this characterization\nis insufficient for a heterostructure containing two different compositions with\npotentially different lattice parameters. Reciprocal space mapping (RSM) or\ntransmission electron microscopy (TEM) would provide more definitive\nevidence of the strain state and film quality. The current XRD data quality also\nappears limited for making strong claims about crystalline quality.\nResponse: Thanks for the professional comment and suggestion. We agree\nwith the reviewer that the direct evidence of compressive strain is needed. In\nthe revised version, we present the newly measured Reciprocal space mapping\n(RSM) of our bilayer LSP thin films on SLAO substrate and present the data\n327\nin Fig. S1a and Fig. R7 below. The results confirm coherent epitaxial strain\nbetween the film and substrate with an in-plane lattice constant of 3.75 Å, and\nthe strain state of the film corresponds to in-plane misfit strain about −2 %.\nMoreover, we also improve the XRD data of our samples and updated it in Fig.\n1b. All these data show that our LSP film has good crystalline quality with\n327\nsufficient compressive strain.\nFig. R7: Reciprocal space mapping around the SrLaAlO (1011) and LSP (1017)\n4 327\nreflections. The film is coherently strained to the substrate.\n3. Hall coefficient interpretation: The positive Hall coefficients observed in this\nwork contrast with recent literature reports showing negative Hall coefficients in\nSr-doped bilayer nickelate films. Given that this heterostructure contains both\nSr and Pr, could the authors provide a more detailed discussion of the charge\ncarrier behavior and how it relates to the superconducting mechanism in their\nspecific system?\nResponse: We thank this reviewer for the careful review. The Hall coefficient\n(R ) in bilayer nickelate thin films indeed shows some kind of contrast in\nH\ndifferent literatures. In bulk crystals under high pressure (see ref. 13), the Hall\ncoefficient is positive and shows clear enhancement when entering the\nsuperconducting state. And in superconducting bilayer thin films，the Hall\ncoefficient of La Ni O (see ref. 36) is positive. However, in La Pr Ni O\n3 2 7 2.85 0.15 2 7\n(see ref. 37) and La Sr Ni O (see ref. 39), the Hall coefficient are negative.\n2.91 0.09 2 7\nRecently, the researchers report an anomalous electron-hole crossover of the\nHall coefficient in superconducting La Sr Ni O thin films with different\n3-x x 2 7-δ\noxygen content (see new ref. 45 in revised version). They found that the R can\nH\nbe simultaneously tuned through Sr doping concentration and oxygen content\nin films. Therefore, the positive R in our bilayer LSP thin film may be due to\nH 327\nthe special doping concentration and oxygen contents. From our calculations,\npresented in Fig.R5 and Supplementary Fig. 13 in the revised manuscript, we\nfind that the β and γ bands give hole - like contribution and the α band around\nΓ point is responsible for the electron-like contribution, and our theoretical\ncalculation show that the largest effect of the pressure for the Fermi surface\nand the bandwidth occurs for the γ pocket. Within purely quasiparticle picture,\nthe Hall coefficient is expected to be small and negative at ambient pressure,\nin agreement with oxygen-rich data of ref.45. The Hall coefficient becomes\npositive as a function of pressure due to increasing volume of the γ-pocket.\nTherefore, based on our present Hall coefficient data on our samples, we may\nconclude that dominant hole-like Hall coefficient at ambient pressure may be a\nresult of certain amount of oxygen deficiency in our samples. In the revised\nmanuscript, we have discussed about the charge carrier behavior more\ncarefully and make some discussions concerning the superconducting\nmechanism. We hope our responses can remove the concerns of this reviewer.\n4. Data presentation: The resistance vs. temperature data should be converted\nto resistivity vs. temperature for proper materials characterization and cross-\ncomparison with others’ work. Additionally, experimental uncertainties should be\nincluded, particularly for the transition temperatures in the phase diagram.\nResponse: Thanks for the contractive suggestions. In the revised version, we\nhave converted the resistance data R(T) into resistivity ρ(T) in Fig.2, Fig.3 and\nSupplementary Fig. 3, Fig. 5a, Fig. 7. The error bars of T s based on the\nc\nuncertainty of the measured temperature are also included in the phase\ndiagram of Fig. 4.\n5. Mechanisms: The manuscript describes two different trends in\nsuperconducting transition behaviour under pressure but does not clearly\nexplain their origins. Could the authors elaborate on what physical mechanisms\ndrive these different behaviours and how they relate to the theoretical\ncalculations?\nResponse: We thank this reviewer for this comment. Our theoretical\ncalculations show a synergic effect of multiband effect in the system by applying\na high pressure. There are two main effects that enhance Cooper pairing in the\nthin films under pressure. First, the reduced c-axis lattice constant leads to a\nstronger presence of the γ-pocket at the Fermi level and its participation in\nCooper pairing with an s±-wave order parameter. Second, pressure increases\nthe hybridization between the 3𝑑 and 3𝑑 orbitals, resulting in greater\n𝑧2 𝑥2−𝑦2\nquasiparticle band coherence. Both effects contribute to the enhancement of\nT . However, the even spin fluctuations are also significantly sensitive to the\nc\nchanges of c-axis lattice constant. Especially, a dome like behavior is seen for\nthe 𝑞𝑒 and 𝑞𝑒 peaks, which is consistent with the experimental observation.\n1 3\nTherefore, it is likely a synergic effect of increased hybridization between\n3𝑑 and 3𝑑 orbitals, resulting in the charge flow between the orbitals\n𝑧2 𝑥2−𝑦2\nand larger itinerancy of the pressurized thin films, together with the enhanced\nantiferromagnetic spin fluctuations both in the in-plane and out-of-plane\nchannels. Moreover, these effects quickly saturate upon larger pressures\nexplaining why no further increase of T and even its reduction is observed.\nc\n6. Reproducibility: While multiple samples are measured, it would be valuable\nto include a more quantitative discussion of sample-to-sample variation in\nsuperconducting properties at ambient pressure, particularly given the\ncomplexity of the heterostructure growth and post-annealing process.\nResponse: We thank this reviewer for this pertinent comment. Actually, all the\nthin film samples in our present study were grown and post-annealed with a\nsimilar process, however, the onset of superconducting transition temperature\nshows some kind of sample dependence. In the revised version, we have\nadded a new Supplementary Note 1 to talk about the details of the synthesis\nprocess and post-annealing parameters of the LSP thin film and give a table\n327\n(see below) to summarize the post annealing parameters and the transport\nproperties of the six films we used in present work. Based on the limited data\nin the table, it seems that more annealing time are important for the good\nmetallic behavior and higher T .\nc\nOzone Flow\nAnnealing T\nc\nSamples pressure rate ρ ρ /ρ\n200K 200K 50K\ntime (h) (K)\n(Pa) (sccm)\nS1 20 10 1.5 38.7 0.163 1.65\nS2 20 10 0.5 31.6 0.259 1.57\nS3 25 20 1.5 38.8 0.217 1.56\nS4 25 20 1 41.4 0.248 1.68\nS5 25 20 2 41.9 0.237 1.86\nS6 20 10 1 38.1 0.285 1.46\nDespite these questions, this work represents a significant contribution to\nunderstanding pressure effects in nickelate superconductors and successfully\ndemonstrates substantial enhancement of transition temperatures through the\ncombination of strain engineering and pressure tuning.\nResponse: We would like to thank this reviewer for the careful review and kind\nappreciation to our work. The constructive suggestions and comments raised\nby the reviewer are very helpful for us to improve our manuscript. With the point-\nto-point responses and related revisions, we hope this reviewer will be satisfied\nwith the revised version.\n--------------------------------------------------------\nResponses to the Report of Reviewer #4\n--------------------------------------------------------\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.\nResponse: We thank this reviewer for the input in reviewing our work. We hope\nthe comments and suggestions raised by this reviewer have been properly\naddressed and answered in our responses to the former three reviewers.\nWe sincerely thank the editor and all four reviewers for their valuable feedback\nthat we have used to improve the quality of our manuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear Authors,\nI appreciate the authors for revisions. However, there are still critical points that\nneed to be revised. Please reconsider following comments.\n1, As for comment 1, the response and revisions are not insufficient. The\ndefinition of the onset superconducting transition temperature should be\nreconsidered. It is still not fair to define the onset critical temperature as defined\nin the revised manuscript. Tc^cross shown in Fig. 2b should be defined as\nTc^onset for a fair comparison. In addition, the definition of Tc^cross in\nsupplementary Fig. 8 seems appropriate for applying the definition of Tc^onset\nas similar as previous studies. The data in Fig. 3b, however, can be interpreted\nvery differently depending on the definition used. When the same definition as\nother papers is applied, the transition temperature shows almost no increase.\nFurthermore, the definition of Tc^cross in Fig. 3b is clearly not valid. The authors\nshould conduct a more fair analysis of the data. There is concern that changing\nthe method of definition could alter the conclusion. For a fair and scientific\ndiscussion, it is important to use a comparable definition to that used in\npreviously reported literature, such as ref. 13 and 40. The authors must revise\nthe definition of the onset temperature.\n2, The response to the comments 2 and 4, the comments of [Therefore, we may\nattribute the increase of normal state resistance to the damage to the electric\nconnection of the film caused by the solidification of the pressure-transmitting\nmedium.] and [Some of the conduction paths of the thin films may be partially\ndestroyed due to change of the pressure environment, such as the solidification\nof the PTM, producing considerable amount of dislocations and defects on the\nfilms.] are provided. These comments appear to be an arbitrary interpretation\nthat changes in the pressure medium cause abnormalities in resistance but\nhave no intrinsic effect on the transition temperature. The basis for drawing this\nconclusion has not been sufficiently explained. If the dislocation is induced in\nthe film by applying pressure, the pressure may not induce the lattice\ncompression because the pressure may be relaxed by inducing dislocation.\nUnder this situation, what does understanding the pressure dependence of the\ntransition temperature lead to? Lattice compression may not be increased as\npressure increases above 8 GPa. In Fig. 4, the decrease above the critical\ntemperature of 8 GPa may be attributed to an extrinsic origin unrelated to the\nincrease in pressure.\nTo explain the pressure dependence of resistivity for general readers, Figure\nR1 should be added in supplementary information.\nIf the authors claim this sentence [We may argue that the weak insulating\nbehavior above Tc at high pressures is an intrinsic property of the bilayer\nnickelate thin films.] in line 281, the results should be compared to the bulk\nstudies of bilayer nickelates although [Such behavior has been reported in the\nunderdoped cuprates48, 49.] is commented.\n3, As for comment 12, Applying pressure causes the thin film and substrate to\ncompress isotropically, so it is reasonable to assume that the a-axis length of\nfilm is also compressed. The proposed calculation model seems not valid.\nFailure to explain the lattice deformation in the computational model to readers\nmay lead to misunderstanding. It should be explicitly stated that the calculation\nassumes a fixed a-axis length and affection of this fixing.\n4, Fig. R2 should be included in supplementary information. If the authors claim\nthe stability of superconductivity in air, in addition to the description about the\nstability in air, the fragility by applying pressure should be also described in main\ntext.\n5, The claims in abstract seem not supported by results. The descriptions\nshould be revised fair to the results.\nThe claim of [Here we report the enhancement of Tc onset from about 40 K to\nover 60 K] in abstract should be revised. By applying appropriate definition for\nfair comparison, judging from the data in Fig. 2b, the temperature seems\nroughly 30 K to over 40 K. In the abstract, the sentence [superconductivity with\nan onset transition temperature (Tconset) over 40 K was achieved in La3Ni2O7\nand (La,Pr)3Ni2O7 thin films at ambient pressure due to in-plane compressive\nstrain.] is also described. However, 40 K in the literature was estimated by an\nappropriate definition, but the author’s definition is not appropriate. In the same\nabstract, it is a critical problem for comparison the onset temperature under\ndifferent definitions. Such description misleads the general readers. The\nauthors should revise their method of definition. The sentence at line 29 of the\nabstract in this manuscript should be revised to [Here we report the\nenhancement of Tconset from about 30 K to over 40 K].\nThe claim of [reaching the maximum Tc onset at about 61.5 K.] in abstract\nshould be revised.\nBy applying appropriate definition for fair comparison, the maximum Tc onset in\nFig. 3b seems roughly 50 K.\nIt would be better to revise the claim of [Our theoretical calculations show that\nthe increase of Tc may be mostly described by the reduction of the c-axis lattice\nconstant, which yields a cooperative enhancement of magnetic fluctuations\nwithin and between the layers and increased metallicity under pressure.],\nbecause he conclusion that the c-axis length is the cause is not logically valid\nin calculations where only the c-axis length is varied. Despite the theoretical\ncalculation under hydrostatic pressure, the authors did not calculate any\nparameters other than the c-axis length in the first place.\nCorrespondingly to the revisions in abstract, the main text should be\nappropriately revised.\n6, in line 138, [a relativity large size (3 mm x 1.5 mm) as shown in the inset of\nFig. 1c] is added. In the inset, the scale bar is necessary to show the sample\nsize.\n7, in line 139, [the applied current is supposed to be uniformly distributed on the\nthin films.] is added in the revision. How did the authors judge uniformity of the\ncurrent? Since it is rather difficult in general to characterize the current\nuniformity in sample, when providing such speculation, it is necessary to explain\nthe experimental basis.\n8, in line 364-370, the claim of the consistency in the sentence of [This is\nconsistent with the Hall coefficient data shown in Fig. 2d, indicating stronger\nmetallicity of the normal state upon applied pressure.] appropriate? The\ndetection of insulating behavior in experimental results seems more important.\nIn this point, the inconsistency seems more important to be noted in the\ndiscussion part.\n9, in line 431-438, the extrinsic origin with inducing dislocation etc has to be\nalso discussed.", "reviewer_2": "The authors have revised the manuscript significantly and its quality is improved.\nTheir replies to all reviewers' questions are satisfactory and I recommend its\npublication in Nature Communication.", "reviewer_3": "The authors have adequately addressed all my concerns and made a lot of\nefforts to improve the quality of the data. I am satisfied with the revisions and\nrecommend this manuscript for publication in Nature Communications.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "Responses to the Reviewers’ report\n(The words in black color are from the Reviewers´ reports, and the blue words\ngive our responses.)\n--------------------------------------------------------\nResponses to the Report of Reviewer #1\n--------------------------------------------------------\nI appreciate the authors for revisions. However, there are still critical points that\nneed to be revised. Please reconsider following comments.\nResponse: We thank this reviewer for the valuable comments/suggestions. We\nhave carefully considered the issues pointed out by this reviewer and revised\nthe related parts. The definition of the transition temperature has been\nreconsidered. The T cross shown in the last version has been defined as T onset,\nc c\nthis definition has been unified through the whole paper for a fair comparison\nbetween our work and the previous published literatures. We hope the\nreviewers are satisfied with the relevant revisions.\n1. As for comment 1, the response and revisions are not insufficient. The\ndefinition of the onset superconducting transition temperature should be\nreconsidered. It is still not fair to define the onset critical temperature as defined\nin the revised manuscript. Tc^cross shown in Fig. 2b should be defined as\nTc^onset for a fair comparison. In addition, the definition of Tc^cross in\nsupplementary Fig. 8 seems appropriate for applying the definition of Tc^onset\nas similar as previous studies. The data in Fig. 3b, however, can be interpreted\nvery differently depending on the definition used. When the same definition as\nother papers is applied, the transition temperature shows almost no increase.\nFurthermore, the definition of Tc^cross in Fig. 3b is clearly not valid. The authors\nshould conduct a more fair analysis of the data. There is concern that changing\nthe method of definition could alter the conclusion. For a fair and scientific\ndiscussion, it is important to use a comparable definition to that used in\npreviously reported literature, such as ref. 13 and 40. The authors must revise\nthe definition of the onset temperature.\nResponse: We thank this reviewer for pointing out this important issue. We\nagree with the reviewer that the definition of the onset superconducting\ntransition temperature should be reconsidered. In the revised manuscript, we\nhave redefined the T onset as the cross-point of the linear extrapolation of normal\nc\nstate and the transition region with resistivity of 80%-90%ρ (see Figs. 2, 3, and\nn\nSupplementary Fig. 8 in the revised version). The transition temperatures in\nphase-diagram (Fig. 4) and the related statement have also been corrected.\nThis indeed gives a solid base for a more fair comparison between our results\nand those in previously reported literatures. We hope this reviewer agrees with\nour new definition in the updated version.\n2. The response to the comments 2 and 4, the comments of [Therefore, we may\nattribute the increase of normal state resistance to the damage to the electric\nconnection of the film caused by the solidification of the pressure-transmitting\nmedium.] and [Some of the conduction paths of the thin films may be partially\ndestroyed due to change of the pressure environment, such as the solidification\nof the PTM, producing considerable amount of dislocations and defects on the\nfilms.] are provided. These comments appear to be an arbitrary interpretation\nthat changes in the pressure medium cause abnormalities in resistance but\nhave no intrinsic effect on the transition temperature. The basis for drawing this\nconclusion has not been sufficiently explained. If the dislocation is induced in\nthe film by applying pressure, the pressure may not induce the lattice\ncompression because the pressure may be relaxed by inducing dislocation.\nUnder this situation, what does understanding the pressure dependence of the\ntransition temperature lead to? Lattice compression may not be increased as\npressure increases above 8 GPa. In Fig. 4, the decrease above the critical\ntemperature of 8 GPa may be attributed to an extrinsic origin unrelated to the\nincrease in pressure.\nTo explain the pressure dependence of resistivity for general readers, Figure\nR1 should be added in supplementary information.\nIf the authors claim this sentence [We may argue that the weak insulating\nbehavior above Tc at high pressures is an intrinsic property of the bilayer\nnickelate thin films.] in line 281, the results should be compared to the bulk\nstudies of bilayer nickelates although [Such behavior has been reported in the\nunderdoped cuprates48, 49.] is commented.\nResponse: We thank this reviewer for these comments. As we responded in\nlast run of review, as well as in the illustration of Figure R1 and Supplementary\nNote 2, for our samples with different PTM (S3 and S4) and different samples\nwith the same PTM (our samples and 112 thin films in ref. 46), the abnormal\nchange of resistivity magnitude always occurs and the critical pressure for this\nphenomenon seems to be quite random and there is no correlation between the\nchange in Tc and absolute value of normal state resistance in thin films for the\nhigh-pressure measurement in the CAC apparatus. Therefore, we believe that\nthe abnormal increase of resistance in our thin films under pressure are most\nlikely due to the extrinsic reasons, for example the creation of some disorders\nor defects. Accordingly, we have added the Figure R1 to the supplementary\ninformation as Supplementary Fig. 9 in the revised manuscript.\nThese disorders or defects may modify the current flow in some regions,\nproduce new scattering centers, thus the general magnitude of resistivity will\nbe strongly influenced, but the transition temperature itself may not change too\nmuch, because it is determined by the onset transition temperature. Thus,\nconcerning the random values of the resistivity under high pressures, here we\nmean the creation of disorders or defects, instead of the dislocations. We agree\nwith the reviewer that the dislocations induced in the film may release some\nlattice compression. Here, we further address this situation by the looking at the\nanalog in 112 thin films under high pressures (ref. 46). The authors there found\nthat the infinite-layer structure is partially destroyed, producing considerable\namount of disorders or defects in a large scale after the high-pressure\nmeasurements. However, the T is monotonically increased to above 30 K. For\nc\nanother example, in Sr-doped La Ni O thin films, the weak insulating behavior\n3 2 7\ncan also be observed although the quality of the film is very high, which means\nthat the weak insulating behavior may be intrinsic in some doping or pressure\nregion. Therefore, we think that the disorders or defects of the film under high\npressures may also induce the broadening of the superconducting transition,\nbut the evolution of T and weak insulating behavior above T can be interpreted\nc c\nas intrinsic pressure effect of the thin films.\nAs for the sentence in line 281, we agree that it is important to compare this\nbehavior with other bilayer structure, such as bulk crystals and thin films.\nHowever, as we responded in the comment 4 in the last run of review, we still\nwant to emphasis that the electronic structures are quite different in the bulk\nsamples and thin films. Although such insulating behavior is not observed in\nbulk samples under pressure, we want to note that, in nickelate\nsuperconducting thin films, the weak insulating behavior was also observed in\nSr-doped La Ni O with dome-like superconducting region [see ref. 39 and 45].\n3 2 7\nWe have added above information to the revised manuscript and we hope\nthis reviewer is satisfied with our responses and related reversions to the\nmanuscript.\n3. As for comment 12, Applying pressure causes the thin film and substrate to\ncompress isotropically, so it is reasonable to assume that the a-axis length of\nfilm is also compressed. The proposed calculation model seems not valid.\nFailure to explain the lattice deformation in the computational model to readers\nmay lead to misunderstanding. It should be explicitly stated that the calculation\nassumes a fixed a-axis length and affection of this fixing.\nResponse: We thank this reviewer for this pertinent comment. In the\nmanuscript, we have clearly stated that the in-plane lattice constant was fixed\nduring the theoretical calculation in the main text (Line 319-325, 388-390, 415-\n418, 427-429, 506-511 in version R1). We agree with the reviewer that a more\ndetailed justification for the assumption of a fixed in-plane lattice parameter\nwould strengthen the connection between the theoretical model and\nexperimental conditions as commented by the reviewer #2 in the last run of\nreview.\nIn the compressively strained thin films, although the thin film and substrate\nwill be compressed simultaneously under pressure, the case is that the external\npressure acts on a lattice already clamped by the substrate (especially there\nare only few unit cells in thin films), so the in-plane lattice constants and the in-\nplane Ni-O-Ni bond angle remain largely fixed [see for example Fig.1 in B.\nSamanta, and A.B. Georgescu, arXiv: 2506.11427 (2025)]. In the\ncompressively strained thin films, the c-axis lattice constant has already\nelongated for 1-2%, thus we assume that the compression is mainly influenced\nthe c-axis lattice constant. In addition, along the c-axis, there is a bilayer block\nwith NiO planes and two rock-salt layers of LaO, therefore it is much more\nsusceptible to the change with pressure. It is anticipated that the in-plane\ncompressing rate is smaller concerning a \"more homogeneous\" a-axis with the\nstiff transition metal-O bonds. Therefore, we assume that the dominant effect\nfrom pressure compared to the ambient state would be a more stronger\nshrinkage of c-axis lattice constant.\nIn the revised manuscript, we have added a new Supplementary Note 3 in\nthe revised manuscript to explain the lattice deformation in the computational\nmodel to readers and given more explanations on the fixed in-plane lattice\nconstant during the theoretical calculations.\n4. Fig. R2 should be included in supplementary information. If the authors claim\nthe stability of superconductivity in air, in addition to the description about the\nstability in air, the fragility by applying pressure should be also described in main\ntext.\nResponse: We thank this reviewer for this comment. In the revised version, we\nhave added the Fig. R2 to Supplementary information as a new Supplementary\nFig. 2. We also add some necessary descriptions on the fragility of\nsuperconductivity in bilayer thin films without this kind of heterostructure in the\nrevised main text. This reads as: “Without this kind of heterostructure, the films\nare pretty easy to deteriorate in air, showing fragility of superconductivity, and\nit is hard to do the subsequent transport measurements especially under high\npressures”. We hope our responses can remove the concerns of this reviewer.\n5. The claims in abstract seem not supported by results. The descriptions\nshould be revised fair to the results.\nThe claim of [Here we report the enhancement of Tc onset from about 40 K to\nover 60 K] in abstract should be revised. By applying appropriate definition for\nfair comparison, judging from the data in Fig. 2b, the temperature seems\nroughly 30 K to over 40 K. In the abstract, the sentence [superconductivity with\nan onset transition temperature (Tconset) over 40 K was achieved in La3Ni2O7\nand (La,Pr)3Ni2O7 thin films at ambient pressure due to in-plane compressive\nstrain.] is also described. However, 40 K in the literature was estimated by an\nappropriate definition, but the author’s definition is not appropriate. In the same\nabstract, it is a critical problem for comparison the onset temperature under\ndifferent definitions. Such description misleads the general readers. The\nauthors should revise their method of definition. The sentence at line 29 of the\nabstract in this manuscript should be revised to [Here we report the\nenhancement of Tconset from about 30 K to over 40 K].\nThe claim of [reaching the maximum Tc onset at about 61.5 K.] in abstract\nshould be revised.\nBy applying appropriate definition for fair comparison, the maximum Tc onset in\nFig. 3b seems roughly 50 K.\nIt would be better to revise the claim of [Our theoretical calculations show that\nthe increase of Tc may be mostly described by the reduction of the c-axis lattice\nconstant, which yields a cooperative enhancement of magnetic fluctuations\nwithin and between the layers and increased metallicity under pressure.],\nbecause he conclusion that the c-axis length is the cause is not logically valid\nin calculations where only the c-axis length is varied. Despite the theoretical\ncalculation under hydrostatic pressure, the authors did not calculate any\nparameters other than the c-axis length in the first place.\nCorrespondingly to the revisions in abstract, the main text should be\nappropriately revised.\nResponse: According to the suggestions proposed by this reviewer, we have\nrevised the abstract and the related main text carefully in the updated version,\nnow the statements in the revised versions (including abstract and main body)\nare well supported by the results.\n6. in line 138, [a relativity large size (3 mm x 1.5 mm) as shown in the inset of\nFig. 1c] is added. In the inset, the scale bar is necessary to show the sample\nsize.\nResponse: The scale bar of the sample size is added.\n7. in line 139, [the applied current is supposed to be uniformly distributed on the\nthin films.] is added in the revision. How did the authors judge uniformity of the\ncurrent? Since it is rather difficult in general to characterize the current\nuniformity in sample, when providing such speculation, it is necessary to explain\nthe experimental basis.\nResponse: We thank the reviewer for this comment. As shown in the Figure\nR1 below, we use a typical five-probe electrode configuration to measure the\nR and R simultaneously. Since the sample size is relatively large with a\nxx xy\nrectangular shape, and the electrodes for applying the current is parallelly made\nin the two terminals, therefore, the current is supposed to be uniformly applied\non the thin films. We agree with the reviewer that it is difficult to characterize\nthe current uniformity in sample, especially under pressures. In the revised\nmanuscript, we have replaced the image in the inset of Fig. 1c with Fig. R1 and\nchanged the statement, and explained the experimental details for the general\nreader.\nFig. R1: The standard five-probe electrode configuration of the thin film sample before\nputting it into the high-pressure cell of PCC. The electrodes for applying the current are\nput on the two terminals with a uniform distribution covering the entire sample.\n8. in line 364-370, the claim of the consistency in the sentence of [This is\nconsistent with the Hall coefficient data shown in Fig. 2d, indicating stronger\nmetallicity of the normal state upon applied pressure.] appropriate? The\ndetection of insulating behavior in experimental results seems more important.\nIn this point, the inconsistency seems more important to be noted in the\ndiscussion part.\nResponse: We thank the reviewer for raising this issue. Under pressure, the\nenhanced itinerancy of electrons can lead to the increase of the metallicity of\nthe film, and this phenomenon is consistent with the Hall coefficient data in the\nlow-pressure region (< 2 GPa). However, Hall coefficient measurements under\nhigher pressure in CAC is challenging. According to the reviewer`s comment,\nwe realize that the observation of weak insulating state under higher pressures\nis indeed more important. In the revised manuscript, we have modified the\nrelated discussions regarding to the weak insulating behavior based on the\ntheoretical calculations. We hope this reviewer will agree with our related\nrevisions and changes to the manuscript.\n9. in line 431-438, the extrinsic origin with inducing dislocation etc has to be\nalso discussed.\nResponse: Thanks for the comment. As we addressed above, we think the\nhigh pressure may induce some disorders or defects, not dislocations. The\ninfluence on the magnitude of global resistivity is understandable. It may give\nweak influence on the onset transition temperature and the weak insulating\nbahevior, as we argued in comment 2 above. We don`t think the pressure\ninduced disorders or defects on the films will cause the weak insulating\nbehavior in our present work. The reasons are as follow: (1) A large amount of\ndisorders or defects in a large scale after the high-pressure measurements was\nalso observed in 112 thin films under pressure, however, there is no weak\ninsulating behavior observed. (2) The weak insulating behavior is also observed\nin over-doped region of Sr-doped La Ni O at ambient pressure although the\n3 2 7\nquality of the thin films is pretty high. Therefore, the weak insulating behavior\nobserved in our present work should originate from the intrinsic pressure effect\nof the sample itself, for example the gradually enhanced correlation effect which\nprovides the tendency for the formation of a density wave order, probably\nassociated with the shift of the γ-pocket with a flat band feature.\nWe have included some discussion concerning this issue in this paragraph.\nWe hope this reviewer will be satisfied with these revisions.\nWe hope this reviewer is satisfied with our point-to-point responses and related\nrevisions, and will make a positive recommendation to our work for publication\nin Nature Communications.\n--------------------------------------------------------\nResponses to the Report of Reviewer #2\n--------------------------------------------------------\nThe authors have revised the manuscript significantly and its quality is improved.\nTheir replies to all reviewers' questions are satisfactory and I recommend its\npublication in Nature Communication.\nResponse: We are grateful for the recognition and kind recommendation to\npublish our work in Nature Communications. The insightful feedback is highly\nvalued and much appreciated.\n--------------------------------------------------------\nResponses to the Report of Reviewer #3\n--------------------------------------------------------\nThe authors have adequately addressed all my concerns and made a lot of\nefforts to improve the quality of the data. I am satisfied with the revisions and\nrecommend this manuscript for publication in Nature Communications.\nResponse: Many thanks for the satisfactory assessment and supportive\nrecommendation! We deeply appreciate the professional guidance that strongly\nenhanced the quality of our manuscript.\n--------------------------------------------------------\nResponses to the Report of Reviewer #4\n--------------------------------------------------------\nI co-reviewed this manuscript with one of the reviewers who provided the listed\nreports. This is part of the Nature Communications initiative to facilitate training\nin peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.\nResponse: We sincerely thank this reviewer for co-reviewing the manuscript.\nHis/her involvement is greatly appreciated, and these insights contribute\nsignificantly to the review process. We hope the comments and suggestions\nraised by this reviewer have been properly addressed and answered in this run\nof review.\nWe sincerely thank the editor and all four reviewers for their valuable feedback\nthat we have used to improve the quality of our manuscript."}, {"round": 3, "reviewer_comments": {"reviewer_1": "Dear Authors,\nI would like to thank the authors for their revisions.\nThe manuscript has been significantly improved, and it is believed that the revised version is quite well for general readers\nowing to a fair comparison with previous literature.", "reviewer_2": "Responses to the Reviewers’ report\n(The words in black color are from the reviewers´ reports, and the blue words\ngive our responses)\n--------------------------------------------------------\nResponses to the Report of Reviewer #1\n--------------------------------------------------------\nIn this manuscript, the authors report on the effect of pressure on the\nsuperconductivity in bilayer nickelate thin films. This study is an important and\ntimely exploration of the connection between the differences between\nsuperconductivity in bulk materials under pressure and it in compressively-\nstrained thin films at ambient pressure. I agree that the sentence in discussion\npage 17 line 356 [The combination of strain engineering and high pressure is\nan essential tool in the research of nickelate superconducting thin films.] While\nthe authors measured four samples under applied pressure, the results are\nquite complicated. The authors could improve the presentation of the data to\nmake it easier to understand. Theoretical calculations provide some insight, but\nthe discussion in this manuscript seems not sufficient to explain the complicated\nresults.\nTo convince the general reader of the claims in this manuscript, it would be\nbetter to make major revisions to improve the paper, such as the addition of\nfigures.\nreviewer is satisfied with our responses and related reversions to the\nmanuscript.\n2. There is no consistent explanation for the strange behaviour that the\ntransition temperature increases with increasing the resistivity. This observation\nmay come from the artifact by applying inadequate definition method discussed\nin comment 1.\nWhile the increase of the transition temperature may be induced by increase of\nFermi surface or other enhancement of interaction, the increase of the\nresistance likely comes from the reduction of charge carrier density and/or\nincrease of scattering. If these phenomena occurs simultaneously in the sample,\nhow did the authors explain consistently for both the increase of transition\ntemperature and resistance? These phenomena are independently discussed\nin the present manuscript, but the consistent explanation is necessary to\nconvince the claim to readers.\nreviewer that the increase of T may be induced by increase of Fermi surface\nc\nor the enhancement of some interactions. The better metallicity in the normal\nstate in low pressure region (see Fig. 2a) may be induced by the enhanced\nitinerancy of the charge carriers. However, we want to point out that the\nabnormal increase of room temperature resistance (R ) may not reflect the\n293 K\nintrinsic properties of the bilayer thin films under high pressure. For instance,\nas shown in Fig. S7, the pressure for the abnormal increase of resistivity (~4\nGPa) is much lower than the pressure for the saturation of T (~8 GPa).\nc\nTherefore, we may attribute the increase of normal state resistance to the\ndamage to the electric connection of the film caused by the solidification of the\npressure-transmitting medium. The reasons are as follows: (1) For different\nruns of experiment (S3 in Fig. 3 and S4 in Fig. S7) on our bilayer thin films, the\nevolution of superconducting transition temperature with pressure is relatively\nconsistent with each other, while the critical pressure for the increase in normal\nstate resistance is quite different. (2) Similar increase of normal state resistance\nunder high pressure were also observed in the infinite layer thin film [see the\ndata in ref. 46: Wang, N. N. et al., Nat. Commun. 13, 4367 (2022)]. However,\nthe T in 112 thin films is monotonically increased without saturation, which may\nc\nindicate that there is no correlation between the change in T and absolute\nc\nvalue of normal state resistance in thin films for the high-pressure measurement\nin CAC apparatus. Therefore, we believe that the abnormal increase of\nresistance in our thin films under pressure are most likely due to the extrinsic\nreasons. To address these issues more clearly for the readers, we have added\nsome necessary explanations in the main text and a new Supplementary Note\n2 in the revised Supplementary Information to discuss the possible reason for\nthe abnormal enhancement of resistance in our high-pressure measurement.\n3. The resistance values at 300 K for four samples in this study should be\ncompared by plotting as a function of pressure to make clear the reproducibility\nof the pressure effect. Whether superconductivity occurs or not is an important\npoint, but it is also important to compare the reproducibility in the resistivity of\nthe normal state before that occurs. It is expected that the resistance variation\nby applying pressure should systematically occur via shorten lattice and\nincrease of Fermi surface. If the authors claim the reproducibility, this point\nshould be clearly explained with additional data plots.", "reviewer_3": "Responses to the Reviewers’ report\n(The words in black color are from the reviewers´ reports, and the blue words\ngive our responses)\n--------------------------------------------------------\nResponses to the Report of Reviewer #1\n--------------------------------------------------------\nIn this manuscript, the authors report on the effect of pressure on the\nsuperconductivity in bilayer nickelate thin films. This study is an important and\ntimely exploration of the connection between the differences between\nsuperconductivity in bulk materials under pressure and it in compressively-\nstrained thin films at ambient pressure. I agree that the sentence in discussion\npage 17 line 356 [The combination of strain engineering and high pressure is\nan essential tool in the research of nickelate superconducting thin films.] While\nthe authors measured four samples under applied pressure, the results are\nquite complicated. The authors could improve the presentation of the data to\nmake it easier to understand. Theoretical calculations provide some insight, but\nthe discussion in this manuscript seems not sufficient to explain the complicated\nresults.\nTo convince the general reader of the claims in this manuscript, it would be\nbetter to make major revisions to improve the paper, such as the addition of\nfigures.\nreviewer is satisfied with our responses and related reversions to the\nmanuscript.\n2. There is no consistent explanation for the strange behaviour that the\ntransition temperature increases with increasing the resistivity. This observation\nmay come from the artifact by applying inadequate definition method discussed\nin comment 1.\nWhile the increase of the transition temperature may be induced by increase of\nFermi surface or other enhancement of interaction, the increase of the\nresistance likely comes from the reduction of charge carrier density and/or\nincrease of scattering. If these phenomena occurs simultaneously in the sample,\nhow did the authors explain consistently for both the increase of transition\ntemperature and resistance? These phenomena are independently discussed\nin the present manuscript, but the consistent explanation is necessary to\nconvince the claim to readers.\nreviewer that the increase of T may be induced by increase of Fermi surface\nc\nor the enhancement of some interactions. The better metallicity in the normal\nstate in low pressure region (see Fig. 2a) may be induced by the enhanced\nitinerancy of the charge carriers. However, we want to point out that the\nabnormal increase of room temperature resistance (R ) may not reflect the\n293 K\nintrinsic properties of the bilayer thin films under high pressure. For instance,\nas shown in Fig. S7, the pressure for the abnormal increase of resistivity (~4\nGPa) is much lower than the pressure for the saturation of T (~8 GPa).\nc\nTherefore, we may attribute the increase of normal state resistance to the\ndamage to the electric connection of the film caused by the solidification of the\npressure-transmitting medium. The reasons are as follows: (1) For different\nruns of experiment (S3 in Fig. 3 and S4 in Fig. S7) on our bilayer thin films, the\nevolution of superconducting transition temperature with pressure is relatively\nconsistent with each other, while the critical pressure for the increase in normal\nstate resistance is quite different. (2) Similar increase of normal state resistance\nunder high pressure were also observed in the infinite layer thin film [see the\ndata in ref. 46: Wang, N. N. et al., Nat. Commun. 13, 4367 (2022)]. However,\nthe T in 112 thin films is monotonically increased without saturation, which may\nc\nindicate that there is no correlation between the change in T and absolute\nc\nvalue of normal state resistance in thin films for the high-pressure measurement\nin CAC apparatus. Therefore, we believe that the abnormal increase of\nresistance in our thin films under pressure are most likely due to the extrinsic\nreasons. To address these issues more clearly for the readers, we have added\nsome necessary explanations in the main text and a new Supplementary Note\n2 in the revised Supplementary Information to discuss the possible reason for\nthe abnormal enhancement of resistance in our high-pressure measurement.\n3. The resistance values at 300 K for four samples in this study should be\ncompared by plotting as a function of pressure to make clear the reproducibility\nof the pressure effect. Whether superconductivity occurs or not is an important\npoint, but it is also important to compare the reproducibility in the resistivity of\nthe normal state before that occurs. It is expected that the resistance variation\nby applying pressure should systematically occur via shorten lattice and\nincrease of Fermi surface. If the authors claim the reproducibility, this point\nshould be clearly explained with additional data plots.", "reviewer_4": "Responses to the Reviewers’ report\n(The words in black color are from the reviewers´ reports, and the blue words\ngive our responses)\n--------------------------------------------------------\nResponses to the Report of Reviewer #1\n--------------------------------------------------------\nIn this manuscript, the authors report on the effect of pressure on the\nsuperconductivity in bilayer nickelate thin films. This study is an important and\ntimely exploration of the connection between the differences between\nsuperconductivity in bulk materials under pressure and it in compressively-\nstrained thin films at ambient pressure. I agree that the sentence in discussion\npage 17 line 356 [The combination of strain engineering and high pressure is\nan essential tool in the research of nickelate superconducting thin films.] While\nthe authors measured four samples under applied pressure, the results are\nquite complicated. The authors could improve the presentation of the data to\nmake it easier to understand. Theoretical calculations provide some insight, but\nthe discussion in this manuscript seems not sufficient to explain the complicated\nresults.\nTo convince the general reader of the claims in this manuscript, it would be\nbetter to make major revisions to improve the paper, such as the addition of\nfigures.\nreviewer is satisfied with our responses and related reversions to the\nmanuscript.\n2. There is no consistent explanation for the strange behaviour that the\ntransition temperature increases with increasing the resistivity. This observation\nmay come from the artifact by applying inadequate definition method discussed\nin comment 1.\nWhile the increase of the transition temperature may be induced by increase of\nFermi surface or other enhancement of interaction, the increase of the\nresistance likely comes from the reduction of charge carrier density and/or\nincrease of scattering. If these phenomena occurs simultaneously in the sample,\nhow did the authors explain consistently for both the increase of transition\ntemperature and resistance? These phenomena are independently discussed\nin the present manuscript, but the consistent explanation is necessary to\nconvince the claim to readers.\nreviewer that the increase of T may be induced by increase of Fermi surface\nc\nor the enhancement of some interactions. The better metallicity in the normal\nstate in low pressure region (see Fig. 2a) may be induced by the enhanced\nitinerancy of the charge carriers. However, we want to point out that the\nabnormal increase of room temperature resistance (R ) may not reflect the\n293 K\nintrinsic properties of the bilayer thin films under high pressure. For instance,\nas shown in Fig. S7, the pressure for the abnormal increase of resistivity (~4\nGPa) is much lower than the pressure for the saturation of T (~8 GPa).\nc\nTherefore, we may attribute the increase of normal state resistance to the\ndamage to the electric connection of the film caused by the solidification of the\npressure-transmitting medium. The reasons are as follows: (1) For different\nruns of experiment (S3 in Fig. 3 and S4 in Fig. S7) on our bilayer thin films, the\nevolution of superconducting transition temperature with pressure is relatively\nconsistent with each other, while the critical pressure for the increase in normal\nstate resistance is quite different. (2) Similar increase of normal state resistance\nunder high pressure were also observed in the infinite layer thin film [see the\ndata in ref. 46: Wang, N. N. et al., Nat. Commun. 13, 4367 (2022)]. However,\nthe T in 112 thin films is monotonically increased without saturation, which may\nc\nindicate that there is no correlation between the change in T and absolute\nc\nvalue of normal state resistance in thin films for the high-pressure measurement\nin CAC apparatus. Therefore, we believe that the abnormal increase of\nresistance in our thin films under pressure are most likely due to the extrinsic\nreasons. To address these issues more clearly for the readers, we have added\nsome necessary explanations in the main text and a new Supplementary Note\n2 in the revised Supplementary Information to discuss the possible reason for\nthe abnormal enhancement of resistance in our high-pressure measurement.\n3. The resistance values at 300 K for four samples in this study should be\ncompared by plotting as a function of pressure to make clear the reproducibility\nof the pressure effect. Whether superconductivity occurs or not is an important\npoint, but it is also important to compare the reproducibility in the resistivity of\nthe normal state before that occurs. It is expected that the resistance variation\nby applying pressure should systematically occur via shorten lattice and\nincrease of Fermi surface. If the authors claim the reproducibility, this point\nshould be clearly explained with additional data plots."}, "author_response": ""}]

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