Superconductivity and suppressed monoclinic distortion in FeTe films enabled by higher-order epitaxy

Domain: physics
Published: 2025-12-05
Editorial outcome: minor_revision

Abstract
Molecular beam epitaxy enables the growth of thin film materials with novel properties and functionalities. Typically, the lattice constants of films and substrates are designed to match to minimise disorders and strains. However, significant lattice mismatches can result in higher-order epitaxy, where commensurate growth occurs with a period defined by integer multiples of the lattice constants. Despite its potential, higher-order epitaxy is rarely used to enhance material properties or induce emergent phenomena. Here, we report single-crystalline FeTe films grown via 6:5 commensurate higher-order epitaxy on CdTe(001) substrates. Scanning transmission electron microscopy reveals self-organised periodic interstitials near the interface, arising from higher-order lattice matching. Synchrotron x-ray diffraction shows that the tetragonal-to-monoclinic structural transition in bulk FeTe is strongly suppressed. Remarkably, these films exhibit substrate-selective two-dimensional superconductivity, likely due to suppressed monoclinic distortion. These findings demonstrate the potential of higher-order epitaxy as a tool to control materials and inducing emergent phenomena.

Introduction
Engineering materials in thin film form not only enhances our understanding of quantum phenomena but also provides knobs to tune material properties. Among various deposition techniques, molecular beam epitaxy (MBE)—a method where films are grown layer by layer with lattice matching to a substrate—is one of the most powerful tools for fabricating a wide variety of thin films and heterostructures. It offers exceptional control over structure and composition, enabling novel properties and functionalities that go beyond those of bulk crystals1–7. In materials engineering, achieving high-quality materials with minimal disorders, such as defects, misorientation and dislocations, is crucial because quantum transport phenomena often favour clean systems with long scattering times3. In contrast, it is widely known that significant lattice mismatches between a film and a substrate can sometimes result in higher-order epitaxy, also referred to as domain-matching epitaxy, where commensurate growth occurs with a long period defined by integer multiples of the lattice constants8–11. Although such growth modes are typically avoided as they introduce unnecessary disorder into crystals, it has recently been suggested that spatially modulated strain, caused by mismatches, can be used to control the topological properties of materials12. Despite its potential, there are few examples of higher-order epitaxy being utilised to enhance materials properties or induce novel quantum phenomena13.

Iron chalcogenides are one of the most attractive materials platforms for studying the interplay between thin films and substrates, as exemplified by the significant enhancement of the superconducting transition temperature Tc in monolayer FeSe grown on SrTiO3 (STO), from a bulk value of 10 K to above 50 K in the monolayer form4. The Fe(Se,Te)(FST) system has attracted significant interest as a candidate topological superconductor driven by strong spin-orbit coupling from Te, where a Majorana zero mode is expected to emerge at the core of vortex14–16. It is also utilised for a building block for an artificial topological superconductor, where FST is proximitised with topological insulators17,18. FeTe is the other end compound of the FST series and is a non-superconducting antiferromagnetic (AFM) metal. It has a tetragonal P4/nmm crystalline structure consisting of van der Waals-stacked iron-chalcogenide square lattices at room temperature (Fig. 1a). FeTe crystals with minimal excess iron amount undergo a transition to the monoclinic P2/m phase at the structural transition temperature Ts ~ 70 K, below which in-plane anisotropy develops (a/b > 1) and the c-axis tilts slightly towards the a-axis (β < 90∘) (Fig. 1b)19. This monoclinic lattice distortion is accompanied by the emergence of a double-stripe AFM order with a magnetic vector Q = (π,0) in the reciprocal space of the tetragonal lattice with two iron atoms per unit cell (UC)20. Neutron scattering experiments reveal that superconductivity emerges when the (π,0) magnetic correlations are suppressed by partly substituting Se for Te, suggesting that the AFM order is detrimental to superconductivity21.

Results
In this paper, we report growth of single-crystalline higher-order epitaxial superconducting FeTe films using the MBE technique grown on cubic zinc-blende CdTe(001) substrates (Fig. 1c), (See Methods and 17 for more details about sample fabrication). For comparison, we also grew FeTe films on cubic perovskite STO(001) substrates (Fig. 1d). FeTe/CdTe films appear to be single-crystalline with the crystalline orientation of FeTe highly aligned to that of CdTe. Figure 1e shows an XRD θ-2θ profile for a typical FeTe/CdTe film. We observe sharp peaks attributed to FeTe (0 0 n) or CdTe (0 0 2m), where n and m are integers, indicating that the FeTe (001) plane is aligned parallel to the substrate normal, i.e., FeTe [001] ∥ CdTe [001]. The high crystalline quality of the film is further supported by a rocking curve for the FeTe (001) reflection. As shown in Fig. 1f, the rocking curve for FeTe/CdTe exhibits a sharp signal with a small full-width at half maximum (FWHM) of 0.6∘, whereas that for FeTe/STO shows a much broader value of 1.8∘. Furthermore, the XRD azimuthal angle φ-scan for the asymmetric FeTe (104) reflection shows a clear 4-fold oscillation, following the same trend as CdTe (115) (Fig. 1g). The result is consistent with the tetragonal crystal structure and indicates a high lateral orientation of the FeTe film, where FeTe [100] ∥ CdTe [110]. This lateral orientation is further confirmed by atomic force microscopy measurements, which reveal well-defined square-patterned steps and terraces with edges aligned to CdTe 〈110〉 (Fig. 1h). Remarkably, FeTe/CdTe films exhibit superconductivity with an onset critical temperature Tc ~ 12 K, whereas FeTe/STO films grown under the exactly same conditions do not show any superconducting onset down to 2 K (Fig. 1i). We note that the zero resistivity in FeTe/CdTe was not achieved in our previous works, where a partial superconducting transition is observed and zero resistivity appears only when FeTe is interfaced with Bi2Te3 17,22. The zero-resistivity in the current work is achieved by further optimizing growth conditions, such as growth rate and Te-annealing temperature and time. While it has been reported that superconductivity in FeTe can be induced by oxygen incorporation, this typically requires aggressive methods such as exposure to atmosphere for weeks or annealing under oxygen flow23,24. To rule out this possibility, we simultaneously synthesised, in-situ Te-capped, and measured those two films within a day. The results suggest that the substrate-selective superconductivity is an intrinsic property of FeTe/CdTe. These observations motivate a detailed investigation into the crystal structure of FeTe/CdTe.

It is worth noting that the in-plane lattice mismatch between FeTe (aFeTe[100] = 0.383 nm) and CdTe (aCdTe[110] = 0.458 nm) is as large as −20%, whereas that between FeTe and STO (aSTO[100] = 0.390 nm) is relatively small at −1.8%. Given this, it is somewhat surprising that FeTe/CdTe films exhibit apparently higher crystalline quality than FeTe/STO films (See Fig. S1 for further characterisation of FeTe/STO). This counterintuitive result can be attributed to higher-order epitaxy, characterised by a 6:5 commensuration between FeTe and CdTe, as we show in the following. Figure 2a displays a cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of the FeTe/CdTe interface viewed from FeTe [100] ∥ CdTe [110] at room temperature. The interface between FeTe and CdTe is clearly resolved with atomic resolution, as indicated by the overlaid cartoons. Figure 2b presents line profiles along cut A (the bottommost layer of FeTe) and B (the topmost layer of CdTe). While the two profiles differ in modulation period due to the substantial lattice mismatch, there are distinct nearest sites where two atoms closely approach each other. These sites recur every 6aFeTe[100] or 5aCdTe[110], as highlighted by the grey-shaded regions in Fig. 2b. This higher-order lattice matching results in a considerably small residual mismatch, calculated as (6aFeTe[100] − 5aCdTe[110]) / 6aFeTe[100] ~ +0.35%. These results confirm the successful realisation of higher-order epitaxy in FeTe/CdTe films.

The higher-order epitaxy appears to be stabilised by the introduction of self-organised interstitials and periodic displacement only near the interface. As highlighted by the red arrows in Fig. 2b, a pair of additional peaks is observed adjacent to the nearest sites. These interstitials, likely intercalated to reduce interfacial energy associated with the higher-order epitaxy, do not belong to the crystal structures of either FeTe or CdTe, breaking the translational symmetry of FeTe. Such periodic interfacial interstitials have not been observed in other van der Waals-epitaxial systems such as FeSe/STO and FeSe/MgO25–27. Typically, higher-order epitaxial films relax the strain through periodic or random dislocations, characterised by Burgers vectors oriented in the in-plane direction10,28,29. However, in the present system, no apparent dislocation is observed at the interface, and both FeTe and CdTe retain their original crystal structure except for the interstitials. Moreover, we found a slight displacement of atoms at certain sites, marked as 2 and 4 in Fig. 2b, from the equilibrium position. This displacement can be viewed as a local strain that is not uniform, but spatially modulates.

We examine a HAADF-STEM image of an FeTe/CdTe interface over a wider observation frame (Fig. 2c). Interestingly, the interstitials at the FeTe/CdTe interface extend slightly along FeTe [001] into a few UCs, forming discernible nodes that periodically recur along FeTe [010], spanning the entire observation window. Figure 2d displays the fast Fourier transform (FFT) image derived from the HAADF-STEM image near the interface, labelled as FFT1 in Fig. 2c. In addition to the Bragg peaks corresponding to FeTe and CdTe, we observe additional peaks associated with the modulation from higher-order epitaxy. To highlight this, Fig. 2e shows a profile integrated along the Qc direction as a function of Qa. Here the horizontal axis is normalised by the reciprocal lattice vector of FeTe, QFeTe. Apart from the primary Bragg peaks, a distinct peak appears at Qa/QFeTe = 1/6, consistent with the modulation period of 6aFeTe[100]. This peak indicates that the interstitials extend coherently over the interface and create intrinsic structural modulation rather than extrinsic effects, such as moiré interference patterns along the electron beam direction. In addition to the primary modulation mode at Qa/QFeTe = 1/6, related modes at Qa/QFeTe = 1/3, 1/2, and 2/3 are faintly resolved. A mode at Qa/QFeTe = 1/12 appears with an intensity somewhat comparable to the 1/6 mode, hinting at the possible involvement of an additional modulation with a period of 12aFeTe[100] in stabilising the interface. When the FFT is performed on the image taken 3 UCs away from the interface (FFT2), the peak at Qa/QFeTe = 1/6 is not discernible. This suggests that the higher-order epitaxy occurs only near the interface, transitioning to the conventional van der Waals epitaxy at a greater distance. Figure 2f schematically illustrates the FeTe/CdTe interface from the top (FeTe [001]), where the interstitial pairs form superlattice along the interface, resulting in a characteristic 6×6 modulation. This modulation is also confirmed by Reflection High Energy Electron Diffraction (RHEED), which reveals additional pronounced peaks corresponding to the superlattice only when a few UCs of FeTe are deposited (Fig. S3). Identifying the chemical nature of the interstitials, however, remains challenging, as their close spacing with other elements exceeds the resolution limits of our current experiments.

As higher-order epitaxy is a characteristic of FeTe/CdTe films, it is tempting to attribute the substrate-selective superconductivity to some consequences resulting from this epitaxy. To access a potential link between the superconductivity and crystal structure at low temperatures, we performed temperature (T)-dependent synchrotron XRD experiments on FeTe films. First, as a reference, we measured a thick FeTe/STO film with a thickness t of 1000 nm, denoted as FeTe1000/STO (Fig. 3a). At T = 100 K, (007) Bragg reflection appears as a single peak in the θ-2θ profile. As T decreases, the intensity of this peak steadily diminishes, while another peak begins to emerge at lower angles (2θ ~ 70.7∘) below Ts ~ 60 K. At a base temperature of 7 K, the higher-angle peak disappears completely, leaving a single peak at the lower angle. This discrete shift in the 2θ peak position is a consequence of the tetragonal-to-monoclinic structural transition, as reported in bulk crystals20,30 (See Fig. S4 for reciprocal space mappings).

Next, we performed θ-2θ XRD scans for thick and thin FeTe/CdTe films with t = 1000 nm (FeTe1000/CdTe) and 40 nm (FeTe40/CdTe), as shown in Fig. 3b, c. Hereafter, FeTet/CdTe denotes a t-nm-thick FeTe film grown on CdTe (100) substrate. In the thick FeTe1000/CdTe film, similar to the FeTe1000/STO film, the lower-angle peak associated with the monoclinic phase develops below Ts. Interestingly, in FeTe1000/CdTe, the higher-angle peak associated with the tetragonal phase remains prominent even below Ts, and the θ-2θ scan reveals a distinct double-peak structure at low temperatures. This double-peak structure indicates the coexistence of tetragonal and monoclinic regions in FeTe1000/CdTe. Notably, the tetragonal phase exhibits a stronger intensity compared to the monoclinic phase, suggesting that, contrary to bulk crystals, the tetragonal phase dominates in FeTe1000/CdTe at low temperatures. The contrasting behaviour observed in FeTe1000/CdTe underscores the critical role of substrate-induced effect, such as cramping, in suppressing monoclinic distortion. Furthermore, in the thin FeTe40/CdTe film, the tetragonal phase is even more dominant, as evidenced by the θ-2θ scans, which shows a single major peak with a slight asymmetry developing below Ts. This asymmetry is attributed to a small portion exhibiting monoclinic distortion. The double Gaussian fitting at each temperature successfully separates the two components in the data.

In Fig. 3d, we summarise the out-of-plane lattice constant c, estimated using single or double Gaussian fittings, as a function of T, alongside values for bulk crystals reported in the literature20,30. At 300 K, the c-values of the films are close to those of the bulk crystals, suggesting that strain from the substrates is minimal. Upon cooling, c of the films decreases, with the largest slope of dc/dT observed in FeTe40/CdTe, indicating a substantial strain effect from CdTe. The variation in dc/dT can be attributed to the difference in thermal expansion between FeTe and the substrates. The smaller lateral thermal expansion of CdTe leads to an effective in-plane tensile strain in FeTe, which in turn enhances the out-of-plane thermal shrinkage in the films (Fig. S5). The Poisson ratios ν of FeTe1000/CdTe and FeTe40/CdTe, evaluated from the dc/dT slope, correspond to 0.4 and 0.5, respectively, showing an enhancement compared to the bulk value of 0.231 (See Supplementary Information for more details). This enhanced Poisson ratio suggests a considerably strong coupling between FeTe and CdTe, which plays a crucial role in achieving the cramping effect that prevents the structural transition. Below Ts, the c-value of FeTe/CdTe films exhibits a clear split, with the tetragonal branch subsisting while a new branch appears in the monoclinic phase, as highlighted in the grey area of Fig. 3d. In this phase, c for all the films appears to approach the bulk value at low temperatures, suggesting complete lattice relaxation free from the strain.

To investigate the impact of substrate effects on the AFM order in FeTe, we performed first-principles calculations, where the in-plane lattice constant was fixed to mimic the substrate constraint (See Methods for more details). With decreasing −Δc/c, which corresponds to the uniaxial compressive strain along the c-axis, the Fe moments (μ) monotonously decreases, while the energy difference between the AFM and paramagnetic ground states, EAFM − EPM, increases (Fig. 3e). This is likely because the compressive strain along the c-axis enhances hopping via Te atoms, reducing electron correlations and making the AFM ordering less favourable. Indeed, in thinner FeTe/CdTe films, anomalies in magnetic susceptibility and the Hall coefficient at Ts, associated with the AFM ordering, become less pronounced17. These results suggest that the AFM ordering is considerably suppressed under the strong compressive strain along the c-axis.

It is informative to estimate the volume fraction of the monoclinic phase, VM/(VT + VM), where VM and VT represent the volumes of the monoclinic and tetragonal phases, respectively, derived from the integrated intensity of each Gaussian component in the θ-2θ profiles. Figure 3f displays the T-dependence of VM/(VT + VM). For FeTe1000/STO, the monoclinic phase sharply develops below Ts and reaches nearly 100% within experimental detection limits below T ~ 30 K. In contrast, the monoclinic phase is significantly suppressed in FeTe/CdTe films, with VM/(VT + VM) reaching about 40% for FeTe1000/CdTe and as low as 15% for FeTe40/CdTe. The VM/(VT + VM) value remains around 40% even for an FeTe200/CdTe film, suggesting that substantial suppression of the monoclinic phase requires films at least thinner than 200 nm (Fig. S6). These results suggest that the suppression of the monoclinic phase is due to the substrate cramping effect, which extends remarkably far into the FeTe film, influencing regions up to 600 nm from the interface in FeTe1000/CdTe, as illustrated in the inset of Fig. 3f. This is somewhat unexpected, as the higher-order epitaxy occurs only within a few UCs near the interface, yet it appears to stabilise the crystal structure over a remarkably large length. This strong coupling between the substrate and the film likely plays a crucial role in the substrate-selective superconductivity, as the strong out-of-plane compressive strain and the suppression of the monoclinic phase weaken the concomitant AFM order, which is known to compete with superconductivity21.

We next investigated the superconducting properties of FeTe/CdTe films and found that they exhibit distinct two-dimensional characteristics. Figure 4a shows the T-dependence of resistivity for t = 10, 20, 40 and 80 nm, where superconductivity is observed in all the films. This observation is consistent with our scenario that the superconductivity can emerge in films with suppressed tetragonal-to-monoclinic transition. Interestingly, the zero-resistivity critical temperature Tc0 decreases with decreasing t, whereas the onset temperature Tc around 12 K is nearly independent of t. This nearly t-independent onset Tc suggests that the energy scale for superconducting gap formation is similar across all films. The broad superconducting transitions observed in thinner films are attributed to the Berezinskii-Kosterlitz-Thouless (BKT) transition, where strong fluctuations due to the low dimensionality prevent long-range order at finite temperatures. As shown in Fig. 4b and Fig. S7a, the temperature dependence of resistivity for the t = 10, 20 and 40 nm films is fitted by the Halperin-Nelson (HN) formula:

R = R0 exp [−2b (T / TBKT − 1)1/2], (1)

where R0 and b are material-dependent fitting parameters32. The fitting for the FeTe40/CdTe film yields TBKT = 5.8 K. The current-voltage (I-V) characteristics for the FeTe40/CdTe film (Fig. 4c) show the power-law behaviour V ∝ Iα, as expected for two-dimensional superconductivity. The inset of Fig. 4c displays the T dependence of the exponent α, which crosses α = 3 at around T = 5.8 K, as expected from the BKT theory.

Two-dimensional superconductivity in thin FeTe/CdTe films is further corroborated by the angle-dependence of the upper critical field Hc2. Figure 4d displays the polar angle θ dependence of Hc2, which is defined by the fields at which R reduces to half of the normal-state value. The Hc2 of the FeTe40/CdTe film exhibits a distinct kink anomaly at θ = 90∘, which is well captured by the two-dimensional Tinkham model, rather than the three-dimensional anisotropic mass model33. In stark contrast, the θ-dependence of Hc2 for the FeTe80/CdTe film agrees well with the three-dimensional model (Fig. S8c). At present, the origin of this crossover in superconducting dimensionality between t = 40 and 80 nm remains unclear. One possible explanation is that the interface hosts two-dimensional superconductivity, whereas the bulk of the FeTe film exhibits three-dimensional superconductivity whose Tc0 exceeds that of the interface for thicknesses above 80 nm. The observation that thin FeTe/CdTe films exhibit two-dimensional superconductivity suggests the crucial role of the substrate effect in the emergence of superconductivity in this system.

The superconductivity observed in FeTe/CdTe is reminiscent of that reported in heterostructure systems where FeTe is interfaced with other tellurides34, such as Bi2Te3-based compounds22,35–37, MnBi2Te438, MnTe39, and Fe3GeTe2 40. Superconductivity has also been observed in FeTe thin films grown via pulsed laser deposition, where tensile strain—similar to that observed in FeTe/CdTe— is argued to be crucial for inducing superconductivity41. However, in all these systems, including heterostructures, structural investigation at low temperatures is lacking. To clarify the mechanism behind the emergence of superconductivity, future investigations are required to determine whether the tetragonal phase is preserved in these heterostructures or not.

Finally, we comment on potential applications of the higher-order epitaxial FeTe films. One major obstacle in investigating Majorana fermions in the topological superconductor candidate FeSe0.45Te0.55 solid solution is the inevitable inhomogeneity associated with Se/Te clustering. ARPES studies have revealed that topological surface states tend to appear in a Te-rich region42, highlighting the essential role of Te atoms in enhancing spin-orbit coupling. Inhomogeneity may also produce trivial conductance peaks at non-zero energies in scanning tunnelling spectroscopy experiments43, which can mimic the zero-bias peaks expected from Majorana zero modes. Additionally, the superconducting properties of FeTe/CdTe appear similar to those of Te-rich FST films: it exhibits Tc ~ 12 K and relatively isotropic upper critical fields (Figs. S7c and S8b), similarly reported in Te-rich FST thin films grown on CdTe44. A recent ARPES study revealed topological surface states in an FeSe0.07Te0.93 thin film45, suggesting that topological states are preserved deep into the FeTe end of the series. These results suggest that the superconducting FeTe, with strong spin-orbit coupling yet free from compositional inhomogeneity, provides an ideal platform for investigating Majorana fermions.

Another intriguing direction of research involves the superlattice of interstitials in FeTe/CdTe, which breaks the translational symmetry of FeTe. Moiré patterns have been observed in one-UC FeTe films grown on Bi2Te346 and NbSe2 47, where 8×2-type and stripe-like patterns, distinct from the present 6×6 pattern on CdTe, are respectively resolved. Such superlattices may generate a long-range moiré-like potential, analogous to effects seen in twisted bilayer graphene48, possibly modifying the electronic structure of the FeTe film near the interface. As higher-order epitaxy can be applied to a wider range of materials systems, our MBE-based technique may provide a more robust and reproducible approach than exfoliation-based method to realising superstructures with periodic strain and potential, opening new ways to control the topological properties of materials and inducing quantum emergent phenomena12,13.

Methods
Sample fabrication
All samples studied in this work were synthesised using the MBE method17. Prior to the synthesis, CdTe(001) substrates were etched with bromine-methanol (0.1% bromine) for 30 seconds, while STO substrates were annealed at 1000∘C for 10 hours under an O2 flow. The films were synthesised at a substrate temperature of 240∘C in an ultrahigh vacuum chamber, with simultaneous beam fluxes of Fe and Te (plus Se for FST). The growth rate was approximately at 3 min/nm. After the growth, a Te-flux was continuously supplied for 30 minutes while samples cooled.

X-ray diffraction
We performed XRD for room-temperature characterisation of samples using SmartLab (RIGAKU) with CuKα x-ray. All other low-temperature XRD data was taken with synchrotron x-rays source (12 keV) at Photon Factory beamline 4C, High Energy Accelerator Research Organization (KEK) in Japan.

Transport
We measured electrical transport properties with Quantum Design Physical Properties Measurement System (PPMS). We used indium soldering for electrical contact to films. The excitation current was fixed at 10 μA.

Scanning transmission electron microscopy
The samples were cut into lamellae using focused ion beam technique and cleaned with Ar ion beam. We performed STEM measurements with acceralation voltage of 200 kV using JEM-ARM200F (JEOL) at Foundation for Promotion of Material Science and Technology of Japan (MST).

First-principles calculations
We performed first-principles calculations to evaluate the impact of c-axis compression on the magnetic properties. The calculations were conducted using the projector augmented wave method implemented in the Vienna ab initio simulation package49, with the generalised-gradient-approximation type exchange-correlation functional proposed by Perdew, Burke, and Ernzerhof50. In our simulations, the lattice parameters were first fixed to the experimental values of the tetragonal phase of Fe1.11Te: a=b=3.8253 Å, c=6.2787 Å, and zTe = 0.2820719. We then systematically reduced the c-axis lattice parameter by x% (x=0.5, 1.0, 1.5, 2.0, and 2.5) keeping all other structural parameters unchanged. All the calculations were performed within the magnetic UC (2×1×1 relative to the primitive cell), using a plane-wave cutoff energy of 500 eV, and a Monkhorst-Pack k-grid of 12×24×12.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Sato et al. reports the so-called “higher-order epitaxy” of FeTe thin films grown on a CdTe substrate using\nmolecular beam epitaxy. The authors present STEM results showing the 6:5 commensurate structure near the interface\nbetween FeTe and CdTe. Their XRD results suggest that the tetragonal-to-monoclinic structural transition is suppressed in\nbulk FeTe when interfaced with CdTe. They further propose that the resulting suppressed monoclinic distortion of FeTe is\nlikely related to the emergence of superconductivity in the FeTe/CdTe heterostructure.\nHowever, the present manuscript suffers from a weak experimental foundation and a highly speculative and unsupported\nhypothesis. It does not meet the criteria for publication in Nature Communications. I therefore do not recommend its\npublication.\n“Higher-order epitaxy” is not a new sample growth mode and has been widely employed in the fabrication of various\nheteroepitaxial materials. In the present work, the authors show a FeTe/CdTe heterostructure with a commensurate structure\nnear their interface, but they provide no compelling experimental evidence that the so-called “high order epitaxy” mode\nextends across the 1000 nm thickness of FeTe. Given the van der Waals nature of FeTe, the growth mode may transition to\nconventional van der Waals epitaxy away from the interface.\nThe authors also hypothesize that the observed superconductivity in the 1000nm FeTe/CdTe heterostructure is likely due to\nsubstrate-induced suppression of the tetragonal-to-monoclinic phase transition in FeTe. While they observe this suppression\nin both the 1000 nm and 40 nm FeTe/CdTe heterostructures, they do not examine superconductivity in the latter sample.\nMoreover, in the scenario of “higher-order epitaxy” grown FeTe, the substrate effects would be expected to be stronger\ncloser to the interface. However, no transport measurements, such as the critical temperatures, are provided to clarify the\ncorrelation between FeTe thickness and superconductivity. This absence of such fundamental characterization undermines\nthe premise of the present work and reveals a striking lack of rigor in experimental design and interpretation.\nEqually concerning is the omission of the authors’ own previous publication on the 15 nm Bi₂Te₃/ 18 nm FeTe/CdTe\nheterostructure (Yasuda et al., Nat. Commun. 10, 2734 (2019)), where superconductivity was also observed. Considered\nalongside the current results, it highlights the need for a more critical elucidation of the proposed correlation between\nsuppression of the tetragonal-to-monoclinic structural transition and superconductivity. The exclusion of their previous work\ngives a misleading impression of novelty and raises questions about scholarly transparency.", "reviewer_2": "The article provides results about the epitaxy on the FeTe on CdTe and STO, revealing a superconductivity emerging at the\ninterface. I am glad to see the results, since the intrinsic superconductivity of FeTe provides many clues for unconventional\nsuperconductivity and for its topological application in quantum computing. That is why this FeTe interfacing system have\nbeen intensively studied in the passed decade, especially, all the results is based on epitaxy thin films, which provides high\nmeaningful potential, as the epitaxy is crucial for realizing large scale controllable fabrication for quantum computing. For the\nmajor results provide by this article, I believe they are convincing, however, to make this article more convincing , especially\non the understanding on the structure surpressing induced superconductivity, i want to see more details before agreeing with\nthe publication.\n1. The rheed pattern during the epitaxy should be included, it help assess the interface quality.\n2. I want to see thickness dependent superconducting results on the FeTe grown on the CdTe, since the superconducting is\nat the interface, it will help for us to understanding the interface effect.\n3. I want to see the thickness dependent structure transition results, it will help for understanding the interface structure\nchange difference with the bulk sample.\n4. About the discussion on the order epitaxy about the FeTe, I think the author didn’t give a full attention on the previous\nresults, especially about the FeTe grown on Bi2Te3, in which moire pattern has been observed. Please provide a more\ncomprehensive discussion based on all the previous results. It is good for the community to further the research."}, "author_response": "Authors’ reply to the comments raised by the Reviewers\nReply to Reviewer #1\nThe manuscript by Sato et al. reports the so-called “higher-order epitaxy” of FeTe\nthin films grown on a CdTe substrate using molecular beam epitaxy. The authors\npresent STEM results showing the 6:5 commensurate structure near the interface\nbetween FeTe and CdTe. Their XRD results suggest that the tetragonal-to-\nmonoclinic structural transition is suppressed in bulk FeTe when interfaced with\nCdTe. They further propose that the resulting suppressed monoclinic distortion of\nFeTe is likely related to the emergence of superconductivity in the FeTe/CdTe\nheterostructure.\nHowever, the present manuscript suffers from a weak experimental foundation and\na highly speculative and unsupported hypothesis. It does not meet the criteria for\npublication in Nature Communications. I therefore do not recommend its publication.\nResponse 1-1:\nWe thank the Reviewer for their careful reading of our manuscript. We\nacknowledge the Reviewer’s concern regarding the weak correlation between\nexperimental results and the proposed scenario in which higher-order epitaxy plays\na central role in the emergence of superconductivity in FeTe/CdTe films. To address\nthis concern, we have performed additional experiments and substantially revised\nthe manuscript to provide stronger experimental evidence and a clearer rationale for\nour interpretation. We believe these new results and revisions significantly\nstrengthen the manuscript, offering clearer insight into the role of the observed\nstructural features in the emergence of superconductivity. All changes in the revised\nversion are highlighted in red. Please find our point-by-point responses below.\n“Higher-order epitaxy” is not a new sample growth mode and has been widely\nemployed in the fabrication of various heteroepitaxial materials.\nResponse 1-2:\nWe agree that higher-order epitaxy is not a new growth mode introduced by our\nstudy. To clarify this point, we have revised the introductory sentence to emphasise\nthat this growth mode has already been widely studied. The revised sentence now\nreads:\n(Main, page 3, line 23):\n“In contrast, it is widely known that significant lattice mismatches between a film\nand a substrate can sometimes result in higher-order epitaxy, also referred to as\ndomain-matching epitaxy, where commensurate growth occurs with a long period\ndefined by integer multiples of the lattice constants [8–11]”.\nIn the present work, the authors show a FeTe/CdTe heterostructure with a\ncommensurate structure near their interface, but they provide no compelling\nexperimental evidence that the so-called “high order epitaxy” mode extends across\nthe 1000 nm thickness of FeTe. Given the van der Waals nature of FeTe, the growth\nmode may transition to conventional van der Waals epitaxy away from the interface.\nResponse 1-3:\nWe agree that it is an important question how far the higher-order epitaxy extends\ninto the FeTe film. As the Reviewer anticipated, our data indicate that the growth\nmode indeed transitions to conventional van der Waals epitaxy away from the\ninterface. This is consistent with the fact, by definition, higher-order epitaxy is\nrelevant only near the interface. This localisation is supported by our cross-sectional\nSTEM measurements, which show that the periodic interstitials are confined to a\nfew unit-cells (UCs) from the interface (red areas in Fig. 2c). Correspondingly, the\nQ/Q = 1/6 modulation becomes negligible just 3 UCs away from the interface (see\na FeTe\n“FFT2” in revised Figs. 2c and 2e), indicating a transition to conventional van der\nWaals epitaxy beyond this depth.\nWe emphasise that although the modulation is localised near the interface, it plays\na significant role in clamping the film, influencing the structural instability of FeTe\nlayer to a depth of up to 600 nm, as revealed by our synchrotron XRD measurements\n(Fig. 3f). To clarify that the periodic interstitials and the associated modulation are\nlocalised at a few UCs from the interface, we have revised the main text as follows.\n(Main, page 5, line 98):\n“The higher-order epitaxy appears to be stabilised by the introduction of self-\norganised interstitials and periodic displacement only near the interface.”\n(Main, page 6, line 128):\n“When the FFT is performed on the image taken 3 UCs away from the interface\n(FFT2), the peak at Q/Q = 1/6 is not discernible. This suggests that the higher-\na FeTe\norder epitaxial growth is confined to the region near the interface, transitioning to\nconventional van der Waals epitaxy at a greater distance.”\n(Main, page 9, line 209):\n“This is somewhat unexpected, as the higher-order epitaxy occurs only within a\nfew UCs near the interface, yet it appears to stabilise the crystal structure over a\nremarkably large length.”\n(Revised) Fig. 2, Real-space observation of self-organised periodic interstitial\nmodulation near FeTe/CdTe interface. a, Cross-sectional HAADF-STEM image near\nan FeTe/CdTe interface. The yellow, brown, and magenta spheres indicate Te, Fe,\nand Cd atoms, respectively. b, Integrated-intensity profiles along the cut A and B\nindicated in a. The dots above the profile indicate the equilibrium position for each\natom. The grey areas indicate the sites where the interfacial ions approach most\nclosely. The red arrows represent the interfacial interstitials. The vertical solid black\nlines represent peak position for the sites 2 and 4, showing a slight modulation from\nthe equilibrium towards the nearest sites. c, Wide area HAADF-STEM image near\nan FeTe/CdTe interface. The red shaded regime indicates the position of the periodic\ninterstitials. The yellow arrows denote the period of modulation, which corresponds\nto 6 unit cells (UCs) of FeTe, which approximately equals to 5UCs of CdTe. Areas\nlabelled as FFT1 and FFT2 correspond to the regions where fast Fourier\ntransformation (FFT) was performed. d, fast Fourier transformation (FFT) FFT\nimage taken within the window indicated as \"FFT\" FFT1 in c. The blue, magenta,\nand red arrows indicate Bragg peaks for FeTe, CdTe, and the interfacial modulation,\nrespectively. e, FFT profiles integrated along Q as a function of Q divided by the\nc a\nwave number Q , corresponding to a Bragg peak of FeTe. The red and black lines\nFeTe\ncorrespond to the results taken in FFT1 and FFT2, respectively. The blue, magenta,\nand red arrows are the same as d, while the grey arrows indicate harmonics of the\ninterfacial modulation, which appear at fractions of Q . f, Top view schematics of\nFeTe\nthe 6×6 superlattice of the interfacial interstitials.\nThe authors also hypothesize that the observed superconductivity in the 1000nm\nFeTe/CdTe heterostructure is likely due to substrate-induced suppression of the\ntetragonal-to-monoclinic phase transition in FeTe. While they observe this\nsuppression in both the 1000 nm and 40 nm FeTe/CdTe heterostructures, they do\nnot examine superconductivity in the latter sample. Moreover, in the scenario of\n“higher-order epitaxy” grown FeTe, the substrate effects would be expected to be\nstronger closer to the interface. However, no transport measurements, such as the\ncritical temperatures, are provided to clarify the correlation between FeTe thickness\nand superconductivity. This absence of such fundamental characterization\nundermines the premise of the present work and reveals a striking lack of rigor in\nexperimental design and interpretation.\nResponse 1-4:\nWe thank the Reviewer for the constructive comment regarding the thickness\ndependence of superconductivity in FeTe. We agree that including such data\nenhances the depth and rigour of our study. In response, we have conducted\nadditional transport experiments on FeTe/CdTe films with varying thicknesses and\nsystematically examined their superconducting properties.\nThese measurements revealed that FeTe/CdTe films exhibit two-dimensional\nsuperconductivity, characterized by Berezinskii-Kosterlitz-Thouless (BKT)\ntransitions and a cusp anomaly in the angular dependence of the upper critical field\nH . Notably, these features are more prominent in thinner films, underscoring the\nc2\nimportance of substrate effects. These results support our interpretation that\nsuperconductivity in FeTe/CdTe is induced by the substrate-mediated suppression\nof the tetragonal-to-monoclinic phase transition.\nWe have included the corresponding data and discussion in the revised manuscript,\nalong with a new figure in the main text.\n(Main, page 9, line 216):\n“We next investigated the superconducting properties of FeTe/CdTe films and found\nthat they exhibit distinct two-dimensional characteristics. Figure 4a shows the T-\ndependence of resistivity for t = 10, 20, 40 and 80 nm, where superconductivity is\nobserved in all the films. This observation is consistent with our scenario that the\nsuperconductivity can emerge in films with suppressed tetragonal-to-monoclinic\ntransition. Interestingly, the zero-resistivity critical temperature T decreases with\nc0\ndecreasing t, whereas the onset temperature T around 12 K is nearly independent\nc\nof t. This nearly t-independent onset T suggests that the energy scale for\nc\nsuperconducting gap formation is similar across all films. The broad\nsuperconducting transitions observed in thinner films are attributed to the\nBerezinskii-Kosterlitz-Thouless (BKT) transition, where strong fluctuations due to\nthe low dimensionality prevent long-range order at finite temperatures. As shown in\nFig. 4b and Extended Data Fig. 7a, the temperature dependence of resistivity for the\nt = 10, 20 and 40 nm films is fitted by the Halperin-Nelson (HN) formula:\n1/2\n𝑅 = 𝑅 exp[−2𝑏(\n𝑇0− 𝑇\n) ],\n0\n𝑇− 𝑇BKT\nwhere R and b are material-dependent fitting parameters [32]. The fitting for the\nBKT\nthe FeTe40/CdTe film (Fig. 4c) show the power-law behaviour 𝑉 ∝ 𝐼𝛼, as expected\nfor two-dimensional superconductivity. The inset of Fig. 4c displays the T\ndependence of the exponent 𝛼, which crosses 𝛼 = 3 at around T = 5.8 K, as\nBKT\nexpected from the BKT theory.\nTwo-dimensional superconductivity in thin FeTe/CdTe films is further\ncorroborated by the angle-dependence of the upper critical field 𝐻 . Figure 4d\nc2\ndisplays the polar angle 𝜃 dependence of 𝐻 , which is defined by the fields at which\nc2\nR reduces to half of the normal-state value. The 𝐻 of the FeTe40/CdTe film\nc2\nexhibits a distinct kink anomaly at 𝜃 = 90°, which is well captured by the two-\ndimensional Tinkham model, rather than the three-dimensional anisotropic mass\nmodel [33]. In stark contrast, the 𝜃-dependence of 𝐻 for the FeTe80/CdTe film\nc2\nagrees well with the three-dimensional model (Extended Data Fig. 8). At present,\nthe origin of this crossover in superconducting dimensionality between t = 40 and 80\nnm remains unclear. One possible explanation is that the interface hosts two-\ndimensional superconductivity, whereas the bulk of the FeTe film exhibits three-\ndimensional superconductivity whose T exceeds that of the interface for\nc0\nthicknesses above 80 nm. The observation that only thin FeTe/CdTe films exhibit\ntwo-dimensional superconductivity underscores the crucial role of the substrate\neffect in the emergence of superconductivity in this system.”\n(New figure) Fig. 4, Two-dimensional superconductivity in FeTe/CdTe films. a,\nTemperature dependence of resistivity with different thickness t. The black and red\narrows indicate the onset and zero-resistivity critical temperatures, T and T ,\nc c0\nrespectively, for the t = 10 nm sample. The inset shows t dependence of T and T .\nc c0\nb,\nTemperature dependence of sheet resistivity of the t = 40 nm thin film on logarithmic\n(main panel) and linear (inset) scales at zero field. The red curve represents fitting\nresult using Halperin-Nelson (HN) formula with T = 5.8 K. c, 𝐼-𝑉 curves in the\nBKT\nlog-log scale taken with 1-ms-pulsed currents. The measurements were performed\nat T = 2-10 K in 1 K increments, and additionally at 5.5 K and 15 K. The dashed\nlines represent linear fittings. The solid black and magenta lines show slopes for 𝑉 ∝\n𝐼 and 𝑉 ∝ 𝐼3, respectively. The inset shows temperature dependence of . The\nexponent crosses  = 3 at around T = 5.8 K. d, Polar angle  dependence of 𝐻 .\nBKT c2\nThe red solid and cyan dashed lines represent the theoretical 2D Tinkham and 3D\nanisotropic mass models, respectively. The inset panel shows an expanded view\naround 𝜃 = 90°. The inset cartoon illustrates the experimental configuration.\n(New figure) Extended Data Fig. 7. Superconducting properties of FeTe/CdTe thin\nfilms. a, Temperature dependence of sheet resistivity on logarithmic scale at zero\nfield for t = 10 and 20 nm. The black curves represent fitting result using Halperin-\nNelson (HN) formula. b, Temperature dependence of sheet resistivity for t = 40 nm\nat zero field (black), in-plane 14 T field (red), and out-of-plane 14 T field (blue). c,\nTemperature dependence of the upper critical field for t = 40 nm, defined as the field\nwhere the sheet resistivity becomes half of the normal state. Lines show the\nWerthamer-Helfand-Hohenberg (WHH) fitting results.\n(Revised) Extended Data Fig. 58, Superconducting upper critical field of an\nFeTe/CdTe film. Three-dimensional superconductivity in an 80-nm-thick FeTe/CdTe\nfilm. a, Temperature dependence of sheet resistivity for a film with t = 80 nm at zero\nfield (black), in-plane 14 T field (red), and out-of-plane 14 T field (blue). b,\nTemperature dependence of the upper critical field, defined as the field where the\nsheet resistivity becomes half of the normal state. Lines show the WHH fitting\nresults. c, Polar angle  dependence of 𝐻 . The red and cyan lines represent the\nc2\ntheoretical 2D Tinkham and 3D anisotropic mass models, respectively. The inset\npanel shows an expanded view around 𝜃 = 90°. The inset cartoon illustrates the\nexperimental configuration.\nEqually concerning is the omission of the authors’ own previous publication on the\n15 nm Bi₂Te₃/ 18 nm FeTe/CdTe heterostructure (Yasuda et al., Nat. Commun. 10,\n2734 (2019)), where superconductivity was also observed. Considered alongside the\ncurrent results, it highlights the need for a more critical elucidation of the proposed\ncorrelation between suppression of the tetragonal-to-monoclinic structural\ntransition and superconductivity. The exclusion of their previous work gives a\nmisleading impression of novelty and raises questions about scholarly transparency.\nResponse 1-5:\nWe apologise for the omission of our previous work on Bi Te /FeTe/CdTe\n2 3\nheterostructures (Yasuda et al., Nat. Commun. 2019). In the original draft, we\nfocused on establishing a general research background on the superconductivity of\nheterostructure systems based on Bi Te and FeTe and thus cited works that marked\n2 3\nkey conceptual advances, such as the first discovery of interfacial superconductivity\nin Bi Te /FeTe (He et al., Nat. Commun. 2014), the hybrid symmetry epitaxial\n2 3\nFeTe/Bi Te where the stacking order is reversed (Yao et al., Nano Lett. 2021), and\n2 3\nsystems involving magnetic topological insulators (Cr,Bi,Sb) Te (Yi et al., Science\n2 3\n2024). In this context, we refrained from citing our own previous study, which\nfocused on nonreciprocal transport in the well-established system Bi Te /FeTe,\n2 3\nwhere the hole transfer from Bi Te to FeTe was proposed to be a key for the\n2 3\nemergence of superconductivity on the basis of the ARPES measurement [ K. Owada\net al., Phys. Rev. B 100, 064518 (2019)].\nHowever, we fully acknowledge that citing the paper Yasuda et al., Nat. Commun.\n(2019) is relevant for contextualizing the present results. Importantly, we note that\nthe superconductivity reported in Yasuda et al., Nat. Commun. (2019) primarily\narises at the interface between Bi Te and FeTe, but not at the FeTe/CdTe interface.\n2 3\nThis is supported by the absence of a superconducting transition in the FeTe/CdTe\ncontrol sample in that work (Fig. R1a). Similarly, in our more recent study (Sato et\nal., Phys. Rev. Matter. 2024), FeTe/CdTe show only a partial superconducting\ntransition without achieving zero resistivity (Fig. R1b).\nIn contrast, the present study is the first to demonstrate a superconducting state\nwith zero resistivity in FeTe/CdTe films, achieved through careful optimisation of\ngrowth conditions. In those films, we could exclude the possibility of charge transfer\nfrom the heterointerface because of the large band gap (~ 1.5 eV) in the insulating\nCdTe substrate. We believe this marks a significant advancement beyond our earlier\nworks.\nFig. R1, Absence of zero-resistivity state in FeTe/CdTe films in our previous works.\na, In Yasuda et al. (Nat. Commun. 2019), FeTe/CdTe(100) shows no superconducting\ntransition, while superconductivity is observed when interfaced with Bi Te . b, In\n2 3\nSato et al. (Phys, Rev. Matter. 2024), FeTe films (x = 0) grown on CdTe(100) exhibit\na partial transition but do not reach zero resistivity.\nIn the revised manuscript, we have included our previous work (Yasuda et al., Nat.\nCommun. 2019) and revised related discussions, as follows.\n(Main, page 4, line 71):\n“The zero resistivity in FeTe/CdTe, which was not reported in our previous works\n[Sato et al., Phys. Rev. Matter. (2024), and Yasuda et al., Nat. Commun. (2019)], is\nachieved by further optimizing growth conditions, such as growth rate and Te-\nannealing temperature and time.\n(Main, page 10, line 248):\n“The superconductivity observed in FeTe/CdTe is reminiscent of that reported in\nheterostructure systems where FeTe is interfaced with other tellurides [34], such as\nBi Te -based compounds [Yasuda et al., Nat. Commun. (2019), 35–37], MnBi Te\n2 3 2 4\n[Yuan et al., Nano Lett. (2024)], MnTe [39], and Fe GeTe [40].\n3 2\nReply to Reviewer #2\nThe article provides results about the epitaxy on the FeTe on CdTe and STO,\nrevealing a superconductivity emerging at the interface. I am glad to see the results,\nsince the intrinsic superconductivity of FeTe provides many clues for unconventional\nsuperconductivity and for its topological application in quantum computing. That is\nwhy this FeTe interfacing system have been intensively studied in the passed decade,\nespecially, all the results is based on epitaxy thin films, which provides high\nmeaningful potential, as the epitaxy is crucial for realizing large scale controllable\nfabrication for quantum computing. For the major results provide by this article, I\nbelieve they are convincing, however, to make this article more convincing, especially\non the understanding on the structure suppressing induced superconductivity, I\nwant to see more details before agreeing with the publication.\nResponse 2-1:\nWe thank the Reviewer for carefully reading our manuscript and recognizing the\nsignificance of our research topic, particularly the superconducting FeTe system,\nwhich is of considerable interest both fundamentally and for potential applications.\nIn response to the concerns raised, we have performed additional experiments and\nrevised the discussion accordingly to strengthen the conclusions of our work and\nimprove its overall clarity and rigour. All changes in the revised version are\nhighlighted in red. Please find our point-by-point responses below.\n1. The rheed pattern during the epitaxy should be included, it help assess the\ninterface quality.\nResponse 2-2:\nWe thank the Reviewer for the suggestion to perform a RHEED study. Interestingly,\nthese experiments reveal not only the smooth surface morphology of our films, but\nalso a superlattice modulation originating from the periodic interfacial interstitials.\nExtended Data Figs. 3a-3d present RHEED patterns, with electron beam parallel to\nCdTe[110], observed from the CdTe substrate, and from FeTe films of 2, 4, and 6 unit\ncells (UCs) in thickness, respectively. Clear streak patterns are resolved in all the\nimages, indicating smooth surface morphology during the growth. Notably, as\nhighlighted by the white arrows, additional streak patterns, most pronounced at 1-\nof the streak intervals for FeTe, consistent with the 6×6 superlattice modulation.\nThis feature can be also faintly visible in the RHEED images with electron beam\nparallel to CdTe[100] (Extended Data Fig. 3f), excluding other potential\nsuperlattices such as 6×1 and 6×2. The modulation streaks disappear as the FeTe\nthickness increases, and its critical thickness coincides with the disappearance of\nthe periodic interstitials observed by cross-sectional STEM (Fig. 2c). These results\nconsistently support the formation of the 6×6 modulation near the interface.\nWe have incorporated the RHEED results in Extended Data and added a\ndiscussion in the main text, as follows:\n(New figure) Extended Data Fig. 3, Higer-order epitaxy observed by RHEED.\nRHEED images taken with the electron beam parallel to a-d, CdTe[110]∥FeTe[100]\nand e-h, CdTe[100] ∥ FeTe[110]. The images correspond to the CdTe substrate (a\nand e), 1 UCs FeTe (b and f), 2 UCs FeTe (c and g), and 6 UCs FeTe (d and h). The\nbottom bars, equally spaced, are guide for eyes, where the magenta and blue bars\ndenote the streak position from CdTe and FeTe, respectively. The white arrows\ndenote the additional streaks, corresponding to the 6×6 modulation. The film\nthicknesses are estimated based on the growth rate and deposition time.\n(Main, page 6, line 132):\n“Figure 2f schematically illustrates the FeTe/CdTe interface from the top (FeTe\n[001]), where the interstitial pairs form superlattice across along the interface,\nresulting in a characteristic 6×6 modulation. This modulation is also confirmed by\nReflection High Energy Electron Diffraction (RHEED), which reveals additional\npronounced peaks corresponding to the superlattice only when a few UCs of FeTe\nare deposited (Extended Data Fig. 3).”\n2. I want to see thickness dependent superconducting results on the FeTe grown on\nthe CdTe, since the superconducting is at the interface, it will help for us to\nunderstanding the interface effect.\nResponse 2-3:\nWe agree that investigating the thickness dependence of superconductivity in\nFeTe/CdTe films is important for understanding the interfacial effect. Accordingly,\nwe have performed additional experiments and incorporated a new Figure 4 along\nwith corresponding discussion in the main text. We believe that these new results\nfurther strengthen the significance of our work.\n(Main, page 9, line 216):\n“We next investigated the superconducting properties of FeTe/CdTe films and\nfound that they exhibit distinct two-dimensional characteristics. Figure 4a shows\nthe T-dependence of resistivity for t = 10, 20, 40 and 80 nm, where superconductivity\nis observed in all the films. This observation is consistent with our scenario that the\nsuperconductivity can emerge in films with suppressed tetragonal-to-monoclinic\ntransition. Interestingly, the zero-resistivity critical temperature T decreases with\nc0\ndecreasing t, whereas the onset temperature T around 12 K remains nearly\nc\nindependent of t. This nearly t-independent onset T suggests that the energy scale\nc\nfor superconducting gap formation is similar across all films. The broad\nsuperconducting transitions observed in thinner films are attributed to the\nBerezinskii-Kosterlitz-Thouless (BKT) transition, where strong fluctuations due to\nthe low dimensionality prevent long-range order at finite temperatures. As shown in\nFig. 4b and Extended Data Fig. 7a, the temperature dependence of resistivity for the\nt = 10, 20 and 40 nm films is fitted by the Halperin-Nelson (HN) formula:\n1/2\n𝑅 = 𝑅 exp[−2𝑏(\n𝑇0− 𝑇\n) ],\n0\n𝑇− 𝑇BKT\nwhere R and b are material-dependent fitting parameters [32]. The fitting for the\nBKT\nthe FeTe40/CdTe film (Fig. 4c) show the power-law behaviour 𝑉 ∝ 𝐼𝛼, as expected\nfor two-dimensional superconductivity. The inset of Fig. 4c displays the T\ndependence of the exponent 𝛼, which crosses 𝛼 = 3 at around T = 5.8 K, as\nBKT\nexpected from the BKT theory.\nTwo-dimensional superconductivity in thin FeTe/CdTe films is further\ncorroborated by the angle-dependence of the upper critical field 𝐻 . Figure 4d\nc2\ndisplays the polar angle 𝜃 dependence of 𝐻 , which is defined by the fields at which\nc2\nR reduces to half of the normal-state value. The 𝐻 of the FeTe40/CdTe film\nc2\nexhibits a distinct kink anomaly at 𝜃 = 90°, which is well captured by the two-\ndimensional Tinkham model, rather than the three-dimensional anisotropic mass\nmodel [33]. In stark contrast, the 𝜃-dependence of 𝐻 for the FeTe80/CdTe film\nc2\nagrees well with the three-dimensional model (Extended Data Fig. 8). At present,\nthe origin of this crossover in superconducting dimensionality between t = 40 and 80\nnm remains unclear. One possible explanation is that the interface hosts two-\ndimensional superconductivity, whereas the bulk of the FeTe film exhibits three-\ndimensional superconductivity whose T exceeds that of the interface for\nc0\nthicknesses above 80 nm. The observation that only thin FeTe/CdTe films exhibit\ntwo-dimensional superconductivity underscores the crucial role of the substrate\neffect in the emergence of superconductivity in this system.”\n(New figure) Fig. 4, Two-dimensional superconductivity in FeTe/CdTe films. a,\nTemperature dependence of resistivity with different thickness t. The black and red\narrows indicate the onset and zero-resistivity critical temperatures, T and T ,\nc c0\nrespectively, for the t = 10 nm sample. The inset shows t dependence of T and T .\nc c0\nb,\nTemperature dependence of sheet resistivity of the t = 40 nm thin film on logarithmic\n(main panel) and linear (inset) scales at zero field. The red curve represents fitting\nresult using Halperin-Nelson (HN) formula with T = 5.8 K. c, 𝐼-𝑉 curves in the\nBKT\nlog-log scale taken with 1-ms-pulsed currents. The measurements were performed\nat T = 2-10 K in 1 K increments, and additionally at 5.5 K and 15 K. The dashed\nlines represent linear fittings. The solid black and magenta lines show slopes for 𝑉 ∝\n𝐼 and 𝑉 ∝ 𝐼3, respectively. The inset shows temperature dependence of . The\nexponent crosses  = 3 at around T = 5.8 K. d, Polar angle  dependence of 𝐻 .\nBKT c2\nThe red solid and cyan dashed lines represent the theoretical 2D Tinkham and 3D\nanisotropic mass models, respectively. The inset panel shows an expanded view\naround 𝜃 = 90°. The inset cartoon illustrates the experimental configuration.\n(New figure) Extended Data Fig. 7. Superconducting properties of FeTe/CdTe thin\nfilms. a, Temperature dependence of sheet resistivity on logarithmic scale at zero\nfield for t = 10 and 20 nm. The black curves represent fitting result using Halperin-\nNelson (HN) formula. b, Temperature dependence of sheet resistivity for t = 40 nm\nat zero field (black), in-plane 14 T field (red), and out-of-plane 14 T field (blue). c,\nTemperature dependence of the upper critical field for t = 40 nm, defined as the field\nwhere the sheet resistivity becomes half of the normal state. Lines show the\nWerthamer-Helfand-Hohenberg (WHH) fitting results.\n(Revised) Extended Data Fig. 58, Superconducting upper critical field of an\nFeTe/CdTe film. Three-dimensional superconductivity in an 80-nm-thick FeTe/CdTe\nfilm. a, Temperature dependence of sheet resistivity for a film with t = 80 nm at zero\nfield (black), in-plane 14 T field (red), and out-of-plane 14 T field (blue). b,\nTemperature dependence of the upper critical field, defined as the field where the\nsheet resistivity becomes half of the normal state. Lines show the WHH fitting\nresults. c, Polar angle  dependence of 𝐻 . The red and cyan lines represent the\nc2\ntheoretical 2D Tinkham and 3D anisotropic mass models, respectively. The inset\npanel shows an expanded view around 𝜃 = 90°. The inset cartoon illustrates the\nexperimental configuration.\n3. I want to see the thickness dependent structure transition results, it will help for\nunderstanding the interface structure change difference with the bulk sample.\nResponse 2-4:\nTo gain better insight into how the structural transition depends on film thickness,\nwe performed additional synchrotron XRD measurements on a 200-nm-thick FeTe\nfilm grown on CdTe (FeTe200/CdTe). As shown in Extended Data Fig. 6a, the 𝜃-\n2𝜃XRD scan clearly resolves a double-peak profile, indicating the coexistence of\ntetragonal and monoclinic phases. The result is similar to that of FeTe1000/CdTe,\nsuggesting that substantial suppression of the monoclinic phase requires films\nthinner than at least 200 nm (Extended Data Figs. 6b-d).\nWe have included the corresponding discussion in the main text and added the\nnew Extended Data Figure, as follows:\n(Main, page 7, line 152):\n“Hereafter, FeTet/CdTe denotes a t-nm-thick FeTe film grown on CdTe(100)\nsubstrate.”\n(Main, page 8, line 204):\n“The 𝑉 /(𝑉 + 𝑉 ) value remains around 40 % even for an FeTe200/CdTe film,\nM T M\nsuggesting that substantial suppression of the monoclinic phase requires films at\nleast thinner than 200 nm (Extended. Data Fig. 6).”\n(Method, page 19, line 473):\n“Indeed, the steeper slope in the temperature dependence of c for FeTe films\nindicates a significant out-of-plane expansion strain from substrates (Fig. 3cd and\nExtended Data Fig. 6b).  for FeTe1000/CdTe, FeTe200/CdTe, and FeTe40/CdTe is\nestimated to be 0.5, 0.45, and 0.4, respectively, which is significantly larger than\n0.21, which was obtained by a first-principles calculation for bulk FeTe [31].”\nExtended Data Fig. 6, Suppression of monoclinic lattice distortion in\nFeTe200/CdTe sample. a, XRD 𝜃-2𝜃 profiles around the FeTe (0 0 7) Bragg\nreflection for FeTe200/CdTe. Each profile is vertically shifted for clarity. Grey and\nred curves are Gaussian fittings for the tetragonal and monoclinic phases,\nrespectively. Vertical dashed lines are guides for eyes. b, Temperature dependence\nof the lattice parameter c deduced from the FeTe (0 0 7) reflections. Orange, cyan,\nblue, and purple markers denote FeTe1000/STO, FeTe1000/CdTe, FeTe200/CdTe,\nand FeTe40/CdTe, respectively. White and black squares are c for bulk single\ncrystals reported by neutron [20] and XRD [30] studies. Cyan, blue, and purple lines\nare simulations for the Poisson ratios  = 0.4, 0.45, and 0.5, respectively, assuming\nperfect clamping to the CdTe substrate. The data highlighted in red and grey areas\nare those for tetragonal and monoclinic phases, respectively. The error bars\nrepresent the standard deviation derived from fittings. c, Temperature dependence\nof the volume fraction of the monoclinic phase, 𝑉 /(𝑉 + 𝑉 ). The lines are guides\nM T M\nfor the eyes. The error bars represent the standard deviation derived from fittings.\nd, Schematics of FeTe/CdTe films with a phase separation into monoclinic and\ntetragonal. The monoclinic phase is considerably suppressed in FeTe40/CdTe.\nWe also performed additional FFT analysis on the cross-sectional STEM image to\nexamine how the periodic interstitial modulation evolves with distance from the\ninterface. We found that the Q/Q = 1/6 modulation becomes negligible beyond\na FeTe\napproximately 3 UCs away from the interface (Revised Figs. 2c and 2e). This result\nindicates that the higher-order epitaxy is only prominent near the interface, and that\nthis superstructure is independent of the overall film thickness as long as it exceeds\na few UCs.\nWe have included the corresponding discussion in the main text, as follows:\n(Main, page 6, line 128):\n“When the FFT is performed on the image taken 3 UCs away from the interface\n(FFT2), the Q/Q = 1/6 modulation becomes negligible. This suggests that the\na FeTe\nhigher-order epitaxial growth is confined to the region near the interface,\ntransitioning to conventional van der Waals epitaxy at a greater distance.”\n(Main, page 9, line 209):\n“This is somewhat unexpected, as the higher-order epitaxy occurs only within a few\nUCs near the interface, yet it appears to stabilise the crystal structure over a\nremarkably large length.”\n(Revised) Fig. 2, Real-space observation of self-organised periodic interstitial\nmodulation near FeTe/CdTe interface. a, Cross-sectional HAADF-STEM image near\nan FeTe/CdTe interface. The yellow, brown, and magenta spheres indicate Te, Fe,\nand Cd atoms, respectively. b, Integrated-intensity profiles along the cut A and B\nindicated in a. The dots above the profile indicate the equilibrium position for each\natom. The grey areas indicate the sites where the interfacial ions approach most\nclosely. The red arrows represent the interfacial interstitials. The vertical solid black\nlines represent peak position for the sites 2 and 4, showing a slight modulation from\nthe equilibrium towards the nearest sites. c, Wide area HAADF-STEM image near\nan FeTe/CdTe interface. The red shaded regime indicates the position of the periodic\ninterstitials. The yellow arrows denote the period of modulation, which corresponds\nto 6 unit cells (UCs) of FeTe, which approximately equals to 5UCs of CdTe. Areas\nlabelled as FFT1 and FFT2 correspond to the regions where fast Fourier\ntransformation (FFT) was performed. d, fast Fourier transformation (FFT) FFT\nimage taken within the window indicated as \"FFT\" FFT1 in c. The blue, magenta,\nand red arrows indicate Bragg peaks for FeTe, CdTe, and the interfacial modulation,\nrespectively. e, FFT profiles integrated along Q as a function of Q divided by the\nc a\nwave number Q , corresponding to a Bragg peak of FeTe. The red and black lines\nFeTe\ncorrespond to the results taken in FFT1 and FFT2, respectively. The blue, magenta,\nand red arrows are the same as d, while the grey arrows indicate harmonics of the\ninterfacial modulation, which appear at fractions of Q . f, Top view schematics of\nFeTe\nthe 6×6 superlattice of the interfacial interstitials.\n4. About the discussion on the order epitaxy about the FeTe, I think the author didn’t\ngive a full attention on the previous results, especially about the FeTe grown on\nBi Te , in which moire pattern has been observed. Please provide a more\n2 3\ncomprehensive discussion based on all the previous results. It is good for the\ncommunity to further the research.\nResponse 2-5:\nWe thank the Referee for highlighting the observation of moiré patterns in FeTe\ngrown on Bi Te , which we had not fully addressed in the original manuscript. To\n2 3\nprovide a more comprehensive discussion of moiré patterns observed in FeTe\nsystems, we have revised the main text, as follows.\n(Main, page 10, line 248):\n“The superconductivity observed in FeTe/CdTe is reminiscent of that reported in\nheterostructure systems where FeTe is interfaced with other tellurides [34], such as\nBi Te -based compounds [Yasuda, Nat. Commun. 2019, 35–37], MnBi Te [Yuan,\n2 3 2 4\nNano Lett. 2024], MnTe [39], and Fe GeTe [40].\n3 2\n(Main, page 11, line 273):\n“Moiré patterns have been observed in one-unit-cell FeTe grown on Bi Te [Qin,\n2 3\nNano Lett. 2021] and NbSe [Deng Chin. Phys. B 2021], where 8 × 2-type and\n2\nstripe-like patterns, distinct from the present 6 × 6 pattern on CdTe, are\nrespectively resolved. The superlattice Such superlattices may generate a long-range\nMmoiré-like potential, analogous to effects seen in twisted bilayer graphene [48],\npossibly modifying the electronic structure of the FeTe film near the interface.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have carefully reviewed the revised manuscript and rebuttal letter by Sato et al.\nThe authors have not provided convincing evidence to address the fundamental flaws\nidentified in the first review. The manuscript continues to promote a speculative\nand possibly incorrect hypothesis that substrate effects are the intrinsic origin of\nsuperconductivity in FeTe/CdTe thin films. Their claim is unsupported by\nestablished knowledge, contradicted by the authors’own data, and internally\ninconsistent.\nTaken together, the manuscript rests on a weak experimental foundation and speculative and misleading interpretation,\nremaining fall well short of the standards required for Nature Communications.\nThe central assertion that superconductivity arises from substrate-induced\nsuppression of the tetragonal-to-monoclinic transition is not substantiated. In FeTe\nthin films and in many heterostructures with interfaces between Te-based\ncompounds and FeTe, superconductivity originates within the FeTe layer. In the\nFeTe/CdTe samples reported here, the observed\nsuperconductivity is far more plausibly explained by percolation during growth,\nstoichiometric tuning in Fe1+yTe, or interface effect, rather than substrate influence.\nFurthermore, the finding that thinner FeTe shows a larger volume fraction of tetragonal\nphase yet lower Tc and Hc2 directly contradicts the authors’main claim.\nThe manuscript also lacks novelty and provides a selective and biased interpretation\non the emergence of superconductivity\nin FeTe interfaced with CdTe.\nSuperconductivity in FeTe/CdTe was already reported in the authors’ earlier\npublications, substantially diminishing the contribution of the present work. The\nomission of their Bi2Te3/FeTe/CdTe paper removes crucial context that would\notherwise expose their inconsistencies with their current interpretation. This\nselective presentation reinforces a predetermined conclusion rather than an\nevidence-based analysis.\nThe classification of superconductivity dimensionality is arbitrary and inconsistent.\nThe authors state that “only thin FeTe/CdTe films exhibit two-dimensional\nsuperconductivity”, designating FeTe40 as “2D superconductivity”and FeTe80\nand FeTe1000 as “3D superconductivity”, yet FeTe1000 shows 2D-like signatures in its\nR(T) curve. Without systematic data\nacross all thicknesses, including I–V characteristics and Hc2(θ) analysis, this\ncategorization is speculative and misleading.", "reviewer_2": "After carefully examined the addin of the new content according to my requirement, I agreed with the publication of this\narticle, as the author provided enough information for understanding the two-dimensional SC emerging at the interface. I\nbelieved this system will interest more works towards to the topological quantum application.", "reviewer_3": "The revised manuscript by Sato et al. has made big improvement to answer the points from Reviewer #1. Before, the\nreviewer said the work did not have enough experiment support, missing data on thickness dependence of\nsuperconductivity, no reference to previous related work, and too much speculation.\nIn this new version, the authors add more structure and transport data. They show that higher-order epitaxy is only near the\ninterface, but still it can affect the stability of FeTe film over several hundred nanometres. This is supported by new STEM\nand synchrotron XRD results. Also, they now present thickness-dependent superconductivity data, including BKT analysis\nand angular critical-field measurement. These results make more clear the role of dimension and substrate. In addition, they\ncite and explain their older Bi₂Te₃/FeTe/CdTe work, so the connection to past research is now clear.\nIn summary, the extra experiments and the longer discussion answer directly the main comments of Reviewer #1. Some\ndetails of the mechanism are still not fully explained, but now the manuscript has much stronger experimental base and is\nmore balanced. I think the authors have already replied well to the concerns of Reviewer #1."}, "author_response": "Authors’ reply to the comments raised by the Reviewers\nReply to Reviewer #1\nI have carefully reviewed the revised manuscript and rebuttal letter by Sato et al.\nThe authors have not provided convincing evidence to address the fundamental flaws\nidentified in the first review. The manuscript continues to promote a speculative and\npossibly incorrect hypothesis that substrate effects are the intrinsic origin of\nsuperconductivity in FeTe/CdTe thin films. Their claim is unsupported by\nestablished knowledge, contradicted by the authors’ own data, and internally\ninconsistent. Taken together, the manuscript rests on a weak experimental\nfoundation and speculative and misleading interpretation, remaining fall well short\nof the standards required for Nature Communications.\nResponse 1-1:\nWe thank the Reviewer for their careful reading of our reply and revised manuscript.\nThe central assertion that superconductivity arises from substrate-induced\nsuppression of the tetragonal-to-monoclinic transition is not substantiated. In FeTe\nthin films and in many heterostructures with interfaces between Te-based\ncompounds and FeTe, superconductivity originates within the FeTe layer. In the\nFeTe/CdTe samples reported here, the observed superconductivity is far more\nplausibly explained by percolation during growth, stoichiometric tuning in Fe1+yTe,\nor interface effect, rather than substrate influence. Furthermore, the finding that\nthinner FeTe shows a larger volume fraction of tetragonal phase yet lower Tc and\nHc2 directly contradicts the authors’ main claim.\nResponse 1-2:\nWe thank the Reviewer for suggesting other possible mechanisms for the\nemergence of superconductivity in FeTe/CdTe. As mentioned by the Reviewer,\nstoichiometric tuning plays an important role in reducing the amount of excess iron\natoms, leading to an enhancement in superconducting properties of Fe(Se,Te).\nHowever, we do not think the degree of stoichiometry is significantly different\nbetween the FeTe films grown on CdTe and SrTiO substrates. To reduce the excess\n3\niron atoms, we adopted the Te-annealing process after the growth of all the films, as\ndescribed in the Methods section. This process is crucial for observing\nsuperconductivity, as highlighted by the absence of superconductivity in the as-\ngrown FeTe film (Fig. R1). However, superconductivity remains absent in the Te-\nannealed FeTe films grown on SrTiO (Fig. 1i). While stoichiometric control is thus\n3\nimportant, this substrate-selective superconductivity suggests that the substrate\nplays a crucial role in stabilising superconductivity in FeTe/CdTe.\nFig. R1. Resistivity-Temperature curves for as-grown and Te-annealed FeTe films.\nThickness is 80 nm for both films.\nRegarding the other possible scenarios, such as percolation or interface effects,\nsuperconductivity would be expected to appear only in a small fraction of the sample.\nHowever, these possibilities are excluded by film-thickness dependence of the super\nconducting critical current density as shown in Fig. R2. We measured the I-V\ncharacteristics of FeTe/CdTe films with thickness t = 10, 20, 40 and 80 nm (Fig. R2a).\nIn thin films with t = 10, 20, and 40 nm, the voltage gradually increases with two-\ndimensional current density j and approaches the Ohmic regime above j. In contrast,\nc\nin the film with t = 80 nm, the voltage remains zero within experimental resolution,\nsuddenly becomes non-zero above j ~ 200 A/m, and exhibits a sharp jump at j ~ 1000\nc\nA/m. Figure R2b shows the t-dependence of j, which displays a linear increase with\nc\nt. This t-linear dependence indicates that the supercurrent flows through the entire\ncross-section of the film, ruling out the possibility of interfacial superconductivity.\nFurthermore, the three-dimensional current density of these samples reaches\napproximately 1 MAcm-2, which is comparable to those reported in FeSe Te films\n0.5 0.5\n[T. Ozaki et al., Nat. Commun. 7, 13036 (2016)]. This indicates that the\nsuperconducting volume fraction in our FeTe/CdTe films is reasonably high,\nexcluding the possibility of percolative superconductivity.\nIn response, we have included the above discussion in Methods and Fig. R2 as Fig.\nS9.\nFig. R2. (Fig. S9) a, I-V characteristics of FeTe films with different film thicknesses\nt. b, Thickness dependence of the 2D critical current density j. The line indicates a\nc\nlinear relation with t.\nThe Reviewer also raised concern about our observation that the thinner FeTe film\n(t = 40 nm), which has a higher volume fraction of the tetragonal phase, shows lower\nT and H . However, while the volume fraction of the tetragonal phase is indeed\nc c2\nlarger in thinner samples, the actual thickness of the tetragonal region is smaller in\nthese samples. Based on our assumption that the tetragonal and monoclinic phases\nseparate along the film-normal direction (inset of Fig. 3f), the effective thickness of\nthe tetragonal phase can be estimated to be approximately 34, 120, and 600 nm for\nfilms with t = 40, 200, and 1000 nm, respectively. Therefore, it is not contradictory\nthat T and H are small for the thinner film with a larger tetragonal volume fraction\nc c2\nbut a smaller effective tetragonal-phase thickness.\nThe manuscript also lacks novelty and provides a selective and biased interpretation\non the emergence of superconductivity in FeTe interfaced with CdTe.\nSuperconductivity in FeTe/CdTe was already reported in the authors’ earlier\npublications, substantially diminishing the contribution of the present work. The\nomission of their Bi2Te3/FeTe/CdTe paper removes crucial context that would\notherwise expose their inconsistencies with their current interpretation. This\nselective presentation reinforces a predetermined conclusion rather than an\nevidence-based analysis.\nResponse 1-3:\nAs stated in the manuscript, in our earlier work, a zero-resistance state was not\nachieved in FeTe/CdTe, which is now realised in the present study through further\noptimization of the growth conditions and post-annealing process. Moreover, the\npresent study reveals unique features that appear only in FeTe/CdTe, namely the\nhigher-order epitaxial interface identified by cross-sectional STEM and the\npronounced suppression of monoclinic distortion demonstrated by synchrotron XRD.\nSince the significance of the present study lies not merely in the observation of\nsuperconductivity but in elucidating its structural origin, we believe that a partial\nsuperconducting transition in FeTe/CdTe in our previous report does not\nsubstantially diminish the novelty or importance of the present study.\nTo clarify this point, we have amended the following sentence in the revised\nmanuscript.\nMain, page 4, line 71:\nWe note that Tthe zero resistivity in FeTe/CdTe , which was not reported achieved\nin our previous works where only partial superconducting transitions were observed,\nand zero resistivity appeared only when FeTe was interfaced with Bi Te [17, 22],.\n2 3\nThe zero-resistivity in the current work is achieved by further optimizing growth\nconditions, such as growth rate and Te-annealing temperature and time.\nThe classification of superconductivity dimensionality is arbitrary and inconsistent.\nThe authors state that “only thin FeTe/CdTe films exhibit two-dimensional\nsuperconductivity”, designating FeTe40 as “2D superconductivity”and FeTe80\nand FeTe1000 as “3D superconductivity”, yet FeTe1000 shows 2D-like signatures in its\nR(T) curve. Without systematic data across all thicknesses, including I–V\ncharacteristics and Hc2(θ) analysis, this categorization is speculative and\nmisleading.\nResponse 1-4:\nAs presented in response 1-2 and Fig. R2, the I-V characteristics of FeTe/CdTe\nfilms provide further supporting evidence for the superconducting dimensional\ncrossover. The thinner films (t = 10-40 nm) exhibit non-zero voltage at relatively low\ncurrent densities, whereas the thicker film (t = 80 nm) exhibits a sharp voltage jump\nat j. These features are consistent with our interpretation of the superconducting-\nc\ndimensional crossover from 2D to 3D as the film thickness increases. Regarding\nFeTe1000, we agree that the R(T) curve shows a slight tail above the zero-resistivity\ntemperature, which looks like a signature of 2D superconductivity. However, we\nspeculate that this feature originates from inhomogeneity across the film, which\nmight be severe in thicker films.\nWe have revised the following sentence to slightly tone down our claim.\nMain, page 10, line 247:\nThe observation that only thin FeTe/CdTe films exhibit two-dimensional\nsuperconductivity underscores suggests the crucial role of the substrate effect in the\nemergence of superconductivity in this system.\nReply to Reviewer #2\nAfter carefully examined the addin of the new content according to my requirement,\nI agreed with the publication of this article, as the author provided enough\ninformation for understanding the two-dimensional SC emerging at the interface. I\nbelieved this system will interest more works towards to the topological quantum\napplication.\nResponse 2-1:\nWe sincerely thank the Reviewer for the positive assessment and for recommending\nthe publication of our manuscript.\nReply to Reviewer #3\nThe revised manuscript by Sato et al. has made big improvement to answer the\npoints from Reviewer #1. Before, the reviewer said the work did not have enough\nexperiment support, missing data on thickness dependence of superconductivity, no\nreference to previous related work, and too much speculation.\nIn this new version, the authors add more structure and transport data. They show\nthat higher-order epitaxy is only near the interface, but still it can affect the stability\nof FeTe film over several hundred nanometres. This is supported by new STEM and\nsynchrotron XRD results. Also, they now present thickness-dependent\nsuperconductivity data, including BKT analysis and angular critical-field\nmeasurement. These results make more clear the role of dimension and substrate.\nIn addition, they cite and explain their older Bi₂Te₃/FeTe/CdTe work, so the\nconnection to past research is now clear.\nIn summary, the extra experiments and the longer discussion answer directly the\nmain comments of Reviewer #1. Some details of the mechanism are still not fully\nexplained, but now the manuscript has much stronger experimental base and is more\nbalanced. I think the authors have already replied well to the concerns of Reviewer\n#1.\nResponse 3-1:\nWe greatly appreciate the Reviewer’s careful and encouraging evaluation. We are\npleased that the additional experiments and extended discussion have been\nrecognised as effectively addressing the previous concerns, and we thank the\nReviewer for recommending our work for publication."}]

Decision letter