# Unconventional Crystal Structure of the High-Pressure Superconductor La 3 Ni 2 O 7

P. Puphal, P. Reiss, N. Enderlein, Y.-M. Wu, G. Khaliullin, V.

Sundaramurthy, T. Priessnitz, M. Knauft, A. Suthar, L. Richter, et al.

► To cite this version:

P. Puphal, P. Reiss, N. Enderlein, Y.-M. Wu, G. Khaliullin, et al., Unconventional Crystal Structure of the High-Pressure Superconductor La 3 Ni 2 O 7. Physical Review Letters, 2024, 133 (14), pp.146002.
10.1103/PhysRevLett.133.146002. [hal-05105619]

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Distributed under a Creative Commons Attribution 4.0 International License
Unconventional Crystal Structure of the High-Pressure Superconductor La₃Ni₂O₇

P. Puphal,¹,∗ P. Reiss,¹,† N. Enderlein,² Y.-M. Wu,¹ G. Khaliullin,¹ V. Sundaramurthy,¹ T. Priessnitz,¹

M. Knauft,¹ A. Suthar,¹ L. Richter,³ M. Isobe,¹ P. A. van Aken,¹ H. Takagi,¹ B. Keimer,¹ Y. E. Suyolcu,¹,‡

B. Wehinger,⁴ P. Hansmann,² and M. Hepting¹,§

¹Max-Planck-Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany

²Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany

³Max-Planck-Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany

⁴European Synchrotron Radiation Facility, 71 Avenue des Martyrs, F-38043 Grenoble, France

<figure><img src="image_2.png" /></figure>

(Received 14 December 2023; revised 11 July 2024; accepted 12 August 2024; published 4 October 2024)

The discovery of high-temperature superconductivity in La₃Ni₂O₇ at pressures above 14 GPa has spurred extensive research efforts. Yet, fundamental aspects of the superconducting phase, including the possibility of a filamentary character, are currently subjects of controversial debates. Conversely, a crystal structure with NiO₆ octahedral bilayers stacked along the c-axis direction was consistently posited in initial studies on La₃Ni₂O₇. Here, we reassess this structure in optical floating zone-grown La₃Ni₂O₇ single crystals that show signs of filamentary superconductivity. Employing scanning transmission electron microscopy and single-crystal x-ray diffraction under high pressures, we observe multiple crystallographic phases in these crystals, with the majority phase exhibiting alternating monolayers and trilayers of NiO₆ octahedra, signifying a profound deviation from the previously suggested bilayer structure. Using density functional theory, we disentangle the individual contributions of the monolayer and trilayer structural units to the electronic band structure of La₃Ni₂O₇, providing a firm basis for advanced theoretical modeling and future evaluations of the potential of the monolayer-trilayer structure for hosting superconductivity.

DOI: 10.1103/PhysRevLett.133.146002

*Introduction*—Layered transition metal oxides manifest a plethora of quantum phenomena, including orbital ordering, complex magnetic states, and unconventional superconductivity [1]. A prevalent structural motif in these materials is either a perovskite or a perovskite-derived crystal lattice, serving as a conducive platform for the emergence of electronic correlations and exotic phase behaviors [2–4]. An archetypal example within this class of materials is the Ruddlesden-Popper (RP) series of ruthenates [5], denoted as (Sr, Ca)ₙ+₁RuₙO₃n+₁, where n is the number of consecutive RuO₆ octahedral layers within a structural unit. The ground state of each compound in this series is determined not only by the choice of the alkaline metal ion [6–11], but also by the layer index n. For instance, the bilayer (BL) compound Sr₃Ru₂O₇ realizes quantum criticality and metamagnetism

[12], whereas trilayer (TL) Sr₄Ru₃O₁₀ displays ferromagnetic behavior [13].

Recently, the RP series of nickelates has experienced a resurgence of interest [14], even though investigations into the Rₙ+₁NiₙO₃n+₁ compounds (R = rare-earth) started over three decades ago [15–17]. The catalyst for this revival are recent high-pressure studies reporting superconductivity in La₃Ni₂O₇ [18] and La₄Ni₃O₁₀ [19–22] with a T_c of around 80 and 20 K, respectively.

Yet, the electronic configuration of the octahedrally coordinated Ni ions in the RP series is markedly distinct from that of the earlier discovered infinite-layer nickelate superconductors [23–27], where Ni ions exhibit a formal 3d⁹ configuration, isoelectronic and isostructural to cuprate superconductors [28,29]. Instead, Ni in La₃Ni₂O₇ possesses an average 3d⁷.⁵ configuration, given the conventional RP structure with stacked BL units [15,30–35]. Notably, this configuration is rather close to the formal 3d⁷ state in perovskite nickelates, which were proposed to exhibit a cupratelike electronic structure when sandwiched between layers of an insulator [36–38]. Furthermore, an average 3d⁷.⁵ state is reminiscent of hole-doped La₂NiO₄, where 3d⁷ and 3d⁸ sites coexist [39–41].

Nevertheless, consensus on the theoretical framework describing the high-T_c superconductivity in La₃Ni₂O₇ has remained elusive. While most models consider the n = 2 RP structure and strong intrabilayer coupling as key

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

<footnote>*Contact author: puphal@fkf.mpg.de</footnote>

<footnote>†Contact author: p.reiss@fkf.mpg.de</footnote>

<footnote>‡Contact author: eren.suyolcu@fkf.mpg.de</footnote>

<footnote>§Contact author: hepting@fkf.mpg.de</footnote>
ingredients, the approaches for disentangling the intermixed multiorbital states in La₃Ni₂O₇ vary. Specifically, the roles assigned to the low-energy Ni 3dₓ²⁻ᵧ² and 3d_z² and O 2p orbital degrees of freedoms diverge among the models, yielding either singletlike states with partial analogies to those of 3d⁹ cuprates [18,42–44] or different notions [45–55].

Moreover, a possibly filamentary nature of the superconducting phase has been reported [56], along with a puzzling variation in the electronic transport properties among different La₃Ni₂O₇ samples, including a broad spectrum of superconducting onset temperatures and whether zero resistance is reached or a residual resistance persists [57–60]. These inconsistencies, previously attributed to oxygen off-stoichiometries in La₃Ni₂O₇±δ and/or varying experimental conditions, underscore the need for further investigations to elucidate the fundamental properties of the material.

In this Letter, we reassess the physical and structural properties of La₃Ni₂O₇ single crystals. While we observe a maximum T_c of 80 K for applied pressures comparable to those in Ref. [18], our scanning transmission electron microscopy (STEM) and single-crystal x-ray diffraction (XRD) experiments reveal a crystal structure composed of alternating monolayer (ML) and TL units of NiO₆ octahedra, deviating from the conventional RP structure with BL units. We contrast our calculated band structure of the ML-TL system with conventional RP nickelates and discuss possible implications for the understanding of La₃Ni₂O₇ and its high-T_c superconductivity.

**Results**—For the synthesis of La₃Ni₂O₇ single crystals, we utilize the optical floating zone (OFZ) technique under high oxygen pressure. We nominally adopt the same growth conditions as reported in Refs. [18,30], including an oxygen partial pressure of 15 bar (see Supplemental Material [61]). Among the as-grown crystals, we observe variances in the physical properties, such as transport behaviors ranging from insulating to metallic [61], which is reminiscent of previous La₃Ni₂O₇±δ powders and crystals with off-stoichiometric oxygen contents [18,31–33,71–73]. A stoichiometric analysis of an as-grown crystal via inductively coupled plasma mass spectroscopy (ICP-OES) and gas extraction reveals a composition of La₂.₉₈(1)Ni₁.₉₉(1)O₆.₈₃(7). On the other hand, we find that annealing of crystals at 600 °C in 600 bar O₂ atmosphere results in samples that exhibit closely consistent physical properties, including metallic transport behavior at ambient pressure [Fig. 1(a)]. Hence, we mostly focus on annealed samples, denoted as La₃Ni₂O₇, in the following.

The evolution of the electrical resistance of an annealed La₃Ni₂O₇ crystal under pressure is displayed in Fig. 1. We employ a Syassen-Holzapfel-type diamond anvil cell (DAC) with CsI as a solid pressure medium and a conventional four-point measurement technique. Once an initial sealing pressure of approximately 3 GPa is applied, the

<figure><img src="image_3.png" /><figcaption>FIG. 1. (a) Pressure and temperature dependence of the electrical resistance of an annealed La₃Ni₂O₇ single crystal. Solid lines were measured upon pressure increase, while the dashed line shows the resistance after decompression to 2.6 GPa, indicating hysteretic behavior. The inset shows the sample inside the gasket hole. (b) Field and current dependence of the resistance at the highest pressure measured. Both the field and the current are applied within the *ab* plane. (c) Pressure-temperature phase diagram of the superconducting phase.</figcaption></figure>

metallic behavior observed in ambient-pressure measurements changes to a semiconducting-like temperature dependence [Fig. 1(a)]. In addition, the magnitude of the sample resistance shows a dramatic enhancement. Both observations are consistent with those reported for a subset of La₃Ni₂O₇ samples in previous high-pressure studies [18,59]. Toward higher pressure, the behavior gradually changes back to metallic, with an increasingly pronounced resistance drop at low temperatures developing from about 8 GPa onward. Figure 1(b) shows the resistance around the drop as a function of applied in-plane magnetic field and in-plane current. With increasing field, the transition temperature is reduced [61], similarly to previous reports [18]. Employing different excitation currents, we observe clear non-Ohmic behavior, but only for temperatures below the drop, demonstrating a nonmetallic conductivity in this regime. Both the field and current dependence are fully consistent with the emergence of a superconducting regime below T_c. Moreover, a current-dependent resistance below the superconducting onset is a strong indicator for filamentary superconductivity, providing a possible explanation for the persisting residual resistance in our and previous experiments [18,59].

Figure 1(c) summarizes the key observations of our high-pressure transport measurements. Upon compression, we identify signatures of superconductivity from 8 GPa onward, with a strong increase of T_c with increasing
<figure><img src="image_4.png" /><figcaption>FIG. 2. (a) Atomic-resolution STEM-HAADF (left) and STEM-ABF image (right) of our OFZ-grown La₃Ni₂O₇ single crystal, exhibiting a stacking sequence of alternating ML and TL units. (b),(c) Crystal structure of annealed La₃Ni₂O₇ with (b) the *Fmmm* unit cell obtained for 0.7 GPa pressure and (c) the *P4/mmm* unit cell obtained for 15 GPa.</figcaption></figure>

pressure. Beyond 12 GPa and up to 17.3 GPa, the value of $T_c$ saturates and remains identical upon both compression and decompression. However, during decompression below 12 GPa, hysteretic behavior occurs, and a $T_c$ as high as 65 K can be resolved down to 5 GPa. Toward lower pressures, $T_c$ suddenly drops to approximately 20 K. Interestingly, a metallic character persists during decompression at least down to 2.6 GPa [dashed line in Fig. 1(a)], which contrasts with the semiconducting behavior during compression in this pressure regime. Hence, both the superconducting and the underlying metallic phase exhibit hysteretic behavior.

Overall, the transport and magnetic properties of our OFZ-grown crystals are remarkably reminiscent of those reported in several previous studies [18,30], which assumed the RP structure with stacked BL units. However, considering that other studies reported achieving a zero-resistance state below $T_c$ [57–59] and given the sensitive influence of parameters such as oxygen content on the material’s physical properties, we employ STEM for a more rigorous investigation of the structural nuances.

Figure 2(a) displays the simultaneously acquired STEM–high-angle annular dark-field (HAADF) and annular bright-field (ABF) images of an annealed La₃Ni₂O₇ crystal. Remarkably, although the structure in Fig. 2(a) is layered, it consists of a sequence of alternating ML and TL blocks. Such an alternating layer stacking is a dramatic departure from the monotonic stacking of BL units, suggested previously [15, 18, 19, 30–35, 57–59, 74–76]. Instead, the observed stacking manifests a polytype structure [77] of the conventional nickelate RP phases. Beyond the high-resolution STEM imaging in Fig. 2(a), we observe that the alternating ML-TL order persists in all investigated regions of the crystal. This suggests that the ML-TL sequence dominates the lattice of this OFZ-grown crystal.

Nevertheless, a large field-of-view STEM-HAADF survey reveals that on larger length scales the ML-TL sequence is occasionally interrupted by regions with deviating stacking orders [61]. Specifically, we observe regions with several subsequent TL units, reminiscent of the RP phase La₄Ni₃O₁₀, as well as a BL block interspersed between two ML units. Yet, extended regions comprised exclusively of BL units, as would be expected according to the conventional RP phase stacking [15, 18, 19, 30–35, 57–59, 74–76], are not detected in our STEM investigation.

To corroborate the ML-TL stacking sequence in our crystals, we turn to high-resolution synchrotron single-crystal XRD. We utilize a membrane-driven DAC with He as the pressure transmitting medium along with an x-ray beam focused down to a few hundred nanometers, locally probing the pressure dependence of the structure. Schematics of the obtained crystal structures are shown in Figs. 2(b) and 2(c), and the detailed results of the single-crystal XRD refinement between 0 and 16 GPa are presented in Fig. 3.

We find that the refined structures of all investigated samples [61] are composed of the ML-TL sequence, consistent with our STEM observations [Fig. 2(a)]. For annealed La₃Ni₂O₇ single crystals under moderate pressure, the best refinement results are achieved for the orthorhombic space group *Fmmm*. The corresponding unit cell [Fig. 2(b)] is characterized by an essentially doubled *c*-axis lattice constant in comparison to the RP bilayer structure, which was associated with the orthorhombic space group *Amam* in Ref. [18]. For pressures of 12.3 GPa and higher, we find that the symmetry of the ML-TL unit cell changes from *Fmmm* to tetragonal *P4/mmm*, concomitant with a reduction of the *a*, *b*, and *c*-axis lattice constants [Fig. 2(c)]. Notably, this transition to a higher-symmetry structure coincides with the significant sharpening of the superconducting transition occurring in the transport at pressures between 12.2 and 13.9 GPa and with the suppression of the hysteretic behavior between compression and decompression [Fig. 1(a) and 1(c)]. For comprehensiveness, we also examine the crystal structure of an as-grown La₃Ni₂O₆.₈₃ crystal. For this oxygen-deficient variant, the XRD refinements yield the tetragonal *P4/mmm* unit cell already at ambient pressure [Fig. 2(c)], while no symmetry change occurs up to at least 20 GPa [61]. Moreover, a resistance drop remains absent in our high-pressure transport measurements up to 17 GPa on an as-grown crystal [61], suggesting that oxygen deficiency is detrimental for the occurrence of superconductivity in this system.

Figure 3(a) displays the compression of the lattice parameters of annealed La₃Ni₂O₇ with increasing pressure, progressing essentially linearly (bulk modulus 186 GPa). Interestingly, within the TL units, the Ni–O–Ni bond angles along the *c*-axis direction maintain a near-constant value of approximately 170° for pressures up to ~6 GPa
<figure><img src="image_5.png" /><figcaption>FIG. 3. (a) Pressure dependence of the lattice constants of an annealed La₃Ni₂O₇ crystal, extracted from high-resolution single-crystal XRD Rietveld refinements. The left and right panels demarcate the symmetry change from orthorhombic *Fmmm* to tetragonal *P4/mmm*. (b) Ni—O—Ni bond angle along the *c*-axis direction in the TL unit. A bond angle of precisely 180° is intrinsic to the refinements in the *P4/mmm* unit cell. (c) Bond distances between Ni and apical O in the ML (yellow symbols) and TL unit (dark to light blue symbols). (d) Bond distances between Ni and in-plane oxygen ions, where distances along the *a*- and *b*-axis directions are color coded in orange and green, respectively.</figcaption></figure>

[Fig. 3(b)], before rapidly approaching 180°, which is reached at 12.3 GPa. This evolution of the Ni—O—Ni bond angle is qualitatively reminiscent of the increase of *T*<sub>c</sub> in the transport data upon compression over the same pressure range [Fig. 1(c)].

On the other hand, the change of the Ni—O—Ni bond angle with an onset at ~6 GPa is not mirrored in the evolution of the Ni—O bond distances in the NiO₆ octahedra [Figs. 3(c) and 3(d)], which follow an almost

linear behavior similarly to the lattice parameter in Fig. 3(a). The octahedral distortions in the ML unit, particularly the asymmetry between the apical Ni—O bond length [Fig. 3(c)] and the in-plane bond lengths [Fig. 3(d)], are comparable to those of the ML in La₂NiO₄ [78]. For the TL unit, while the asymmetry between the outermost apical Ni—O bond and the in-plane distances is similar to that of the ML unit, its magnitude sequentially decreases for Ni—O bonds approaching the TL unit’s center.

To elucidate the electronic structure of the ML-TL system, we performed density functional theory (DFT) calculations for La₃Ni₂O₇ with a *P*/4*mmm* unit cell and ML-TL stacking according to the XRD refinement for 12.3 GPa pressure. Figure 4(a) shows the band structure and partial density of states (DOS) with a focus on the high-symmetry path Γ—X—*M*—Γ in the *k*<sub>*z*</sub> = 0 plane. The dispersion along the *k*<sub>*z*</sub> direction is negligible. Consistent with previous calculations for RP nickelates with BL or TL stacking [75,79], the states in proximity to the Fermi level are mainly of Ni 3*d* character, which we resolve into 3*d*<sub>*x*<sup>2</sup>—*y*<sup>2</sup></sub> (blue) and 3*d*<sub>*z*<sup>2</sup></sub> (red) contributions. An exception around Γ is the first band above the Fermi level, which exhibits strong La 5*d* character. Furthermore, O 2*p* character is admixed to most Ni bands, although the major spectral weight of the O 2*p* DOS is situated more than 2 eV below the Fermi level [61].

From Γ to *M* along the diagonal *k*<sub>*x*</sub> = *k*<sub>*y*</sub> direction, the orbital characters segregate into almost pure *d*<sub>*x*<sup>2</sup>—*y*<sup>2</sup></sub> and *d*<sub>*z*<sup>2</sup></sub> states. In addition, these Ni bands can be disentangled according to their origins in specific structural units. For the case of *d*<sub>*z*<sup>2</sup></sub> bands, we highlight an isolated ML band at the *M* point in Fig. 4(a), along with three bands originating from the TL unit, corresponding to bonding (+), non-bonding (0), and antibonding (−) linear combinations. Notably, the TL<sup>+</sup> band resides just below the Fermi level at the *M* point, reminiscent of the *d*<sub>*z*<sup>2</sup></sub> flat bands identified in prior DFT studies of RP nickelates with either BL or TL stacking [75,79]. The exact positioning of this band, however, is sensitive to the inclusion of a mean-field *U* parameter [75,79].

Figure 4(b) displays the Fermi surface (FS) in the *k*<sub>*z*</sub> = 0 plane, color coded according to the contributions of *d*<sub>*x*<sup>2</sup>—*y*<sup>2</sup></sub> and *d*<sub>*z*<sup>2</sup></sub> states. Four distinct features in the FS are two circular pockets (β and ε) enclosing Γ, along with square-shaped (γ) and rounded (α) pockets centered around *M*. Moreover, we observe the duplication features α' and β'. The α, β, and γ sheets in Fig. 4(b) are qualitatively similar to those observed for La₄Ni₃O₁₀ with TL stacking [79], while a duplication of FS features (α' and β') was also reported in calculations assuming BL stacking [75]. In the latter calculation, the γ sheet is pushed below the Fermi level as a result of the inclusion of a mean-field *U*. In consequence, the ε sheet around Γ appears to be the distinguishing feature of the FS of the ML-TL system.
<figure><img src="image_6.png" /><figcaption>FIG. 4. DFT results for La₃Ni₂O₇ in the high-pressure P4/mmm phase of the ML-TL structure. (a) The left panel shows the band structure with *d*<sub>*z*</sub>² and *d*<sub>*x*²−*y*²</sub> bands colored in red and blue, respectively, while other bands are colored in gray. The labels ML and TL indicate the structural unit from which each band originates, with the superscripts marking antibonding (−), nonbonding (0), and bonding (+) states around the *M* point. The right panel shows the partial density of states (DOS). (b) FS contour plot for *k*<sub>*z*</sub> = 0 with four sheets (*α*, *β*, *γ*, and *ε*) and duplicate features (*α*' and *β*''). (c) Contributions to the FS, disentangled according to the orbital states (*d*<sub>*z*</sub>² or *d*<sub>*x*²−*y*²</sub>²) and Ni sites within the structural units (ML Ni, inner Ni, and outer Ni).</figcaption></figure>

This unique sheet exhibits an almost pure *d*<sub>*z*</sub>² orbital character [Fig. 4(b)] and originates from the TL<sup>0</sup> band of the outer Ni layer [Fig. 4(c)]. Conversely, the *α*, *α*′ and *β*, *β*′ sheets generally exhibit a mixed orbital character and contributions from both structural units, except for the *k*<sub>*x*</sub> = *k*<sub>*y*</sub> direction. Besides the *ε* sheet, also the *γ* sheet with *d*<sub>*z*</sub>² character is quite isolated, originating solely from the ML unit. Notably, the weights of the *d*<sub>*x*²−*y*²</sub>² and *d*<sub>*z*</sub>² orbital states arising from the ML unit in Fig. 4(c) are distributed differently from the corresponding FS features of the ML in hole-doped R<sub>2</sub>NiO<sub>4</sub>, which exhibits a small *d*<sub>*z*</sub>²-derived electron pocket around Γ and a large hole FS of *d*<sub>*x*²−*y*²</sub>² character [40].

**Discussion**—The findings of our study carry several profound implications. First, the manifestation of the ML-TL stacking in La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> single crystals is remarkable in its own right. This pattern with alternating units from different RP phases extending over macroscopic length scales is distinct from common intergrowth phenomena in RP crystals, where micrometer-sized lamellae of each phase grow atop of each other [80]. A rare previous example of unconventional stacking akin to the ML-TL order of La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> was observed in iridates, where for carefully chosen growth conditions neither the Sr<sub>2</sub>IrO<sub>4</sub> nor Sr<sub>3</sub>Ir<sub>2</sub>O<sub>7</sub> phase forms but a single crystal with alternating ML-BL stacking [81].

More commonly, systems with structurally distinct building blocks have previously been realized in thin film samples grown by layer-by-layer deposition techniques [82,83]. Yet, thin films with RP phases often suffer from stacking faults, and achieving atomically sharp interfaces in “superlattices” composed of distinct building blocks remains a significant challenge [84]. This is particularly evident in LaNiO<sub>3</sub>-LaAlO<sub>3</sub> superlattices, where pronounced chemical intermixing across interfaces occurs in samples nearing the ML limit [85], which were initially

conceptualized as a model system for modified 3d<sup>7</sup> nickelates that exhibit a single-sheet *d*<sub>*x*²−*y*²</sub>² FS [36,37], mimicking that of superconducting cuprates.

In our La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> crystals, the interfaces between the ML and TL structural units are atomically sharp and without visible lattice defects [Fig. 2(a)], but a multiorbital character pervades most of the FS components [Figs. 4(b) and 4(c)]. Hence, the ML-TL architecture is likely not akin to nickelate superlattices aiming to realize a single-sheet *d*<sub>*x*²−*y*²</sub>² FS. Nonetheless, the ML unit is structurally (Fig. 2) and electronically (Fig. 4) quite isolated, offering a compelling point of comparison with the ML in R<sub>2</sub>NiO<sub>4</sub> [39–41]. Accordingly, in spite of certain similarities to conventional RP nickelates, the electronic structure of the ML-TL system stands out as unique. To accurately classify it within the diverse array of nickelates, cuprates, and related materials, further theoretical and experimental studies are required.

In summary, we have revealed that the ML-TL structure manifests as the primary bulk phase in our OFZ-grown La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> single crystals, whereas the conventional RP phase with BL stacking was not detected. However, we also observed minority phases with stacking architectures other than ML-TL, suggesting that distinct admixtures of various stacking orders might be present in individual crystals, which could be a key factor causing the previously reported sample-to-sample variations, in addition to the known oxygen off-stoichiometries.

Utilizing a range of experimental techniques, we identified notable correlations between electrical transport properties and structural parameters, especially between the pressure dependence of *T*<sub>c</sub> [Fig. 1(c)] and the evolution of the Ni—O—Ni bond angle [Fig. 3(b)]. Additionally, we detected a dramatic increase of the normal state resistance upon application of pressure and a filamentary superconducting transition with finite resistance at lowest
temperatures. These observations suggest that not only the superconducting phase, but also the metallic conductance in the pressurized normal state might originate from filamentary channels, which could be either embedded within or in close contact to the majority ML-TL bulk matrix. Also, it cannot be fully ruled out that these behaviors originate from a minority phase, such as undetected BL stacks, a combination of ML, BL, and TL units, or at interfaces between these units. Yet, in such scenarios, the origin of any filamentary nature remains enigmatic within the scope of our study. Nevertheless, our results offer additional intriguing possibilities for the superconducting host phase, which call for future explorations using advanced theoretical models and spectroscopic methods.

*Note added*—Recently, we became aware of a report that observed a similar ML-TL stacking order in OFZ-grown La₃Ni₂O₇ crystals [62].

*Acknowledgments*—We thank A. V. Boris for fruitful discussions, T. Poreba for gas loading a pressure cell for XRD measurements, S. Hammoud for carrying out the ICP-OES measurement, and A. Schulz for assisting with sample characterization at an early stage of the project. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities. The hardware is funded by the German Research Foundation (DFG).

*Data availability*—Data are available [86].

[1] D. I. Khomskii, Transition Metal Compounds (Cambridge University Press, Cambridge, England, 2014).

[2] E. Dagotto, Science **309**, 257 (2005).

[3] R. Mitchell, Mineral Mag. **67**, 419 (2003).

[4] G. Nirala, D. Yadav, and S. Upadhyay, J. Adv. Ceram. **9**, 129 (2020).

[5] G. Cao, C. Alexander, S. McCall, J. Crow, and R. Guertin, Mater. Sci. Eng. B **63**, 76 (1999).

[6] M. Braden, G. André, S. Nakatsuji, and Y. Maeno, Phys. Rev. B **58**, 847 (1998).

[7] A. Jain, M. Krautloher, J. Porras, G. H. Ryu, D. P. Chen, D. L. Abernathy, J. T. Park, A. Ivanov, J. Chaloupka, G. Khaliullin, B. Keimer, and B. J. Kim, Nat. Phys. **13**, 633 (2017).

[8] T. Feldmaier, P. Strobel, M. Schmid, P. Hansmann, and M. Daghofer, Phys. Rev. Res. **2**, 033201 (2020).

[9] H. Trepka, T. Keller, M. Krautloher, J. Xu, K. Habicht, M. Böhm, B. Keimer, and M. Hepting, Phys. Rev. Res. **4**, 023181 (2022).

[10] Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, and F. Lichtenberg, Nature (London) **372**, 532 (1994).

[11] A. Pustogow, Y. Luo, A. Chronister, Y.-S. Su, D. A. Sokolov, F. Jerzembeck, A. P. Mackenzie, C. W. Hicks, N. Kikugawa, S. Raghu, E. D. Bauer, and S. E. Brown, Nature (London) **574**, 72 (2019).

[12] S. A. Grigera, R. S. Perry, A. J. Schofield, M. Chiao, S. R. Julian, G. G. Lonzarich, S. I. Ikeda, Y. Maeno, A. J. Millis, and A. P. Mackenzie, Science **294**, 329 (2001).

[13] M. K. Crawford, R. L. Harlow, W. Marshall, Z. Li, G. Cao, R. L. Lindstrom, Q. Huang, and J. W. Lynn, Phys. Rev. B **65**, 214412 (2002).

[14] M. Hepting, Nature (London) **621**, 475 (2023).

[15] M. Greenblatt, Curr. Opin. Solid State Mater. Sci. **2**, 174 (1997).

[16] J. Rodriguez-Carvajal, M. T. Fernandez-Diaz, and J. L. Martinez, J. Phys. Condens. Matter **3**, 3215 (1991).

[17] J. B. Torrance, P. Lacorre, A. I. Nazzal, E. J. Ansaldo, and C. Niedermayer, Phys. Rev. B **45**, 8209 (1992).

[18] H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M. Zhang, and M. Wang, Nature (London) **621**, 493 (2023).

[19] H. Sakakibara, M. Ochi, H. Nagata, Y. Ueki, H. Sakurai, R. Matsumoto, K. Terashima, K. Hirose, H. Ohta, M. Kato, Y. Takano, and K. Kuroki, Phys. Rev. B **109**, 144511 (2024).

[20] Q. Li, Y.-J. Zhang, Z.-N. Xiang, Y. Zhang, X. Zhu, and H.-H. Wen, Chin. Phys. Lett. **41**, 017401 (2024).

[21] M. Zhang, C. Pei, X. Du, Y. Cao, Q. Wang, J. Wu, Y. Li, Y. Zhao, C. Li, W. Cao, S. Zhu, Q. Zhang, N. Yu, P. Cheng, J. Zhao, Y. Chen, H. Guo, L. Yang, and Y. Qi, arXiv: 2311.07423

[22] Y. Zhu et al., Nature (London) **631**, 531 (2024).

[23] D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Nature (London) **572**, 624 (2019).

[24] Y. Nomura and R. Arita, Rep. Prog. Phys. **85**, 052501 (2022).

[25] M. Hepting, M. P. M. Dean, and W.-S. Lee, Front. Phys. **9**, 808683 (2021).

[26] H. Chen, A. Hampel, J. Karp, F. Lechermann, and A. J. Millis, Front. Phys. **10**, 835942 (2022).

[27] K. Held, L. Si, P. Worm, O. Janson, R. Arita, Z. Zhong, J. M. Tomczak, and M. Kitatani, Front. Phys. **9**, 810394 (2022).

[28] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, Nature (London) **518**, 179 (2015).

[29] P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. **78**, 17 (2006).

[30] Z. Liu, H. Sun, M. Huo, X. Ma, Y. Ji, E. Yi, L. Li, H. Liu, J. Yu, Z. Zhang, Z. Chen, F. Liang, H. Dong, H. Guo, D. Zhong, B. Shen, S. Li, and M. Wang, Sci. China Phys. Mech. Astron. **66**, 217411 (2022).

[31] Z. Zhang, M. Greenblatt, and J. Goodenough, J. Solid State Chem. **108**, 402 (1994).

[32] S. Taniguchi, T. Nishikawa, Y. Yasui, Y. Kobayashi, J. Takeda, S.-i. Shamoto, and M. Sato, J. Phys. Soc. Jpn. **64**, 1644 (1995).

[33] C. D. Ling, D. N. Argyriou, G. Wu, and J. Neumeier, J. Solid State Chem. **152**, 517 (2000).

[34] V. Voronin, I. Berger, V. Cherepanov, L. Gavrilova, A. Petrov, A. Ancharov, B. Tolochko, and S. Nikitenko, Nucl. Instrum. Methods Phys. Res., Sect. A **470**, 202 (2001).
[35] G. Wu, J. J. Neumeier, and M. F. Hundley, Phys. Rev. B **63**, 245120 (2001).

[36] J. Chaloupka and G. Khaliullin, Phys. Rev. Lett. **100**, 016404 (2008).

[37] P. Hansmann, X. Yang, A. Toschi, G. Khaliullin, O. K. Andersen, and K. Held, Phys. Rev. Lett. **103**, 016401 (2009).

[38] A. V. Boris, Y. Matiks, E. Benckiser, A. Frano, P. Popovich, V. Hinkov, P. Wochner, M. Castro-Colin, E. Detemple, V. K. Malik, C. Bernhard, T. Prokscha, A. Suter, Z. Salman, E. Morenzoni, G. Cristiani, H.-U. Habermeier, and B. Keimer, Science **332**, 937 (2011).

[39] M. Uchida, Y. Yamasaki, Y. Kaneko, K. Ishizaka, J. Okamoto, H. Nakao, Y. Murakami, and Y. Tokura, Phys. Rev. B **86**, 165126 (2012).

[40] M. Uchida, K. Ishizaka, P. Hansmann, X. Yang, M. Sakano, J. Miyawaki, R. Arita, Y. Kaneko, Y. Takata, M. Oura, A. Toschi, K. Held, A. Chainani, O. K. Andersen, S. Shin, and Y. Tokura, Phys. Rev. B **84**, 241109(R) (2011).

[41] M. Uchida, K. Ishizaka, P. Hansmann, Y. Kaneko, Y. Ishida, X. Yang, R. Kumai, A. Toschi, Y. Onose, R. Arita, K. Held, O. K. Andersen, S. Shin, and Y. Tokura, Phys. Rev. Lett. **106**, 027001 (2011).

[42] Q. Qin and Y. F. Yang, Phys. Rev. B **108**, L140504 (2023).

[43] Y. F. Yang, G. M. Zhang, and F. C. Zhang, Phys. Rev. B **108**, L201108 (2023).

[44] W. Wú, Z. Luo, D.-X. Yao, and M. Wang, Sci. China Phys. Mech. Astron. **67**, 117402 (2024).

[45] Z. Luo, X. Hu, M. Wang, W. Wú, and D.-X. Yao, Phys. Rev. Lett. **131**, 126001 (2023).

[46] V. Christiansson, F. Petocchi, and P. Werner, Phys. Rev. Lett. **131**, 206501 (2023).

[47] F. Lechermann, J. Gondolf, S. Bötzel, and I. M. Eremin, Phys. Rev. B **108**, L201121 (2023).

[48] M. Nakata, D. Ogura, H. Usui, and K. Kuroki, Phys. Rev. B **95**, 214509 (2017).

[49] Y. Gu, C. Le, Z. Yang, X. Wu, and J. Hu, arXiv:2306.07275.

[50] X. Chen, P. Jiang, J. Li, Z. Zhong, and Y. Lu, arXiv:2307.07154.

[51] D. A. Shilenko and I. V. Leonov, Phys. Rev. B **108**, 125105 (2023).

[52] C. Lu, Z. Pan, F. Yang, and C. Wu, Phys. Rev. B **110**, 094509(2024).

[53] Y. Zhang, L.-F. Lin, A. Moreo, and E. Dagotto, Phys. Rev. B **108**, L180510 (2023).

[54] H. Oh and Y.-H. Zhang, Phys. Rev. B **108**, 174511 (2023).

[55] H. Lange, L. Homeier, E. Demler, U. Schollwöck, F. Grusdt, and A. Bohrdt, Phys. Rev. B **109**, 045127 (2024).

[56] Y. Zhou, J. Guo, S. Cai, H. Sun, P. Wang, J. Zhao, J. Han, X. Chen, Q. Wu, Y. Ding, M. Wang, T. Xiang, H.-k. Mao, and L. Sun, arXiv:2311.12361.

[57] G. Wang, N. N. Wang, X. L. Shen, J. Hou, L. Ma, L. F. Shi, Z. A. Ren, Y. D. Gu, H. M. Ma, P. T. Yang, Z. Y. Liu, H. Z. Guo, J. P. Sun, G. M. Zhang, S. Calder, J.-Q. Yan, B. S. Wang, Y. Uwatoko, and J.-G. Cheng, Phys. Rev. X **14**, 011040 (2024).

[58] Y. Zhang, D. Su, Y. Huang, H. Sun, M. Huo, Z. Shan, K. Ye, Z. Yang, R. Li, M. Smidman, M. Wang, L. Jiao, and H. Yuan, Nat. Phys. **20**, 1269 (2024).

[59] J. Hou, P.-T. Yang, Z.-Y. Liu, J.-Y. Li, P.-F. Shan, L. Ma, G. Wang, N.-N. Wang, H.-Z. Guo, J.-P. Sun, Y. Uwatoko, M. Wang, G.-M. Zhang, B.-S. Wang, and J.-G. Cheng, Chin. Phys. Lett. **40**, 117302 (2023).

[60] X. Sui, X. Han, H. Jin, X. Chen, L. Qiao, X. Shao, and B. Huang, Phys. Rev. B **109**, 205156 (2024).

[61] See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.133.146002 for further details, which includes Refs. [62–70], for additional information.

[62] X. Chen, J. Zhang, A. S. Thind, S. Sharma, H. LaBollita, G. Peterson, H. Zheng, D. P. Phelan, A. S. Botana, R. F. Klie, and J. F. Mitchell, J. Am. Chem. Soc. **146**, 3640 (2024).

[63] P. Puphal, V. Sundaramurthy, V. Zimmermann, K. Küster, U. Starke, M. Isobe, B. Keimer, and M. Hepting, APL Mater. **11**, 081107 (2023).

[64] B.-X. Wang, S. Rosenkranz, X. Rui, J. Zhang, F. Ye, H. Zheng, R. F. Klie, J. F. Mitchell, and D. Phelan, Phys. Rev. Mater. **2**, 064404 (2018).

[65] H. Zheng, B.-X. Wang, D. Phelan, J. Zhang, Y. Ren, M. Krogstad, S. Rosenkranz, R. Osborn, and J. Mitchell, Crystals **10**, 557 (2020).

[66] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo et al., J. Phys. Condens. Matter **21**, 395502 (2009).

[67] P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni et al., J. Phys. Condens. Matter **29**, 465901 (2017).

[68] F. Jollet, M. Torrent, and N. Holzwarth, Comput. Phys. Commun. **185**, 1246 (2014).

[69] M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, Comput. Phys. Commun. **226**, 39 (2018).

[70] M. Kawamura, Y. Gohda, and S. Tsuneyuki, Phys. Rev. B **89**, 094515 (2014).

[71] Y. Kobayashi, S. Taniguchi, M. Kasai, M. Sato, T. Nishioka, and M. Kontani, J. Phys. Soc. Jpn. **65**, 3978 (1996).

[72] T. Fukamachi, K. Oda, Y. Kobayashi, T. Miyashita, and M. Sato, J. Phys. Soc. Jpn. **70**, 2757 (2001).

[73] V. V. Poltavets, K. A. Lokshin, T. Egami, and M. Greenblatt, Mater. Res. Bull. **41**, 955 (2006).

[74] M. Zhang, C. Pei, Q. Wang, Y. Zhao, C. Li, W. Cao, S. Zhu, J. Wu, and Y. Qi, J. Mater. Sci. Technol. **185**, 147 (2024).

[75] J. Yang et al., Nat. Commun. **15**, 4373 (2024).

[76] T. Hosoya, K. Igawa, Y. Takeuchi, K. Yoshida, T. Uryu, H. Hirabayashi, and H. Takahashi, J. Phys. Conf. Ser. **121**, 052013 (2008).

[77] A. Guinier, G. B. Bokij, J. M. Cowley, S. Durovic, H. Jagodzinski, P. Krishna, P. M. de Wolff, B. B. Zvyagin, D. E. Cox, P. Goodman, T. Hahn, K. Kuchitsu, and S. C. Abrahams, Acta Crystallogr. Sect. A **40**, 399 (1984).

[78] A. Mehta and P. J. Heaney, Phys. Rev. B **49**, 563 (1994).

[79] H. Li, X. Zhou, T. Nummy, J. Zhang, V. Pardo, W. E. Pickett, J. F. Mitchell, and D. S. Dessau, Nat. Commun. **8**, 704 (2017).

[80] R. Fittipaldi, D. Sisti, A. Vecchione, and S. Pace, Cryst. Growth Des. **7**, 2495 (2007).
[81] H. Kim, J. Bertinshaw, J. Porras, B. Keimer, J. Kim, J.-W. Kim, J. Kim, J. Kim, G. Noh, G.-Y. Kim, S.-Y. Choi, and B. J. Kim, Phys. Rev. Res. **4**, 013229 (2022).

[82] F. Wrobel, B. Geisler, Y. Wang, G. Christiani, G. Logvenov, M. Bluschke, E. Schierle, P. A. van Aken, B. Keimer, R. Pentcheva, and E. Benckiser, Phys. Rev. Mater. **2**, 035001 (2018).

[83] J. A. Mundy et al., Nature (London) **537**, 523 (2016).

[84] Y. E. Suyolcu, G. Christiani, P. A. van Aken, and G. Logvenov, J. Supercond. Novel Magn. **33**, 107 (2020).

[85] F. Wrobel, A. F. Mark, G. Christiani, W. Sigle, H.-U. Habermeier, P. A. van Aken, G. Logvenov, B. Keimer, and E. 3, Appl. Phys. Lett. **110**, 041606 (2017).

[86] 10.15151/ESRF-ES-1304268675