The trilayer nickelate exhibits frustrated superconductivity with competing interlayer pairings.
The superconductivity has a complex doublet order parameter like the Higgs field in particle physics.
The frustration reduces its superconducting Tc by over half compared to that of bilayer nickelates.
The interlayer pairing causes a Josephson frequency half that of usual intralayer pairing superconductors.
| [1] | Sun, H., Huo, M., Hu, X., et al. (2023). Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621: 493−498. DOI: 10.1038/s41586-023-06408-7. |
| [2] | Hou, J., Yang, P.-T., Liu, Z.-Y., et al. (2023). Emergence of high-temperature superconducting phase in the pressurized La3Ni2O7 crystals. Chin. Phys. Lett. 40: 117302. DOI: 10.1088/0256-307X/40/11/117302. |
| [3] | Zhang, Y., Su, D., Huang, Y. et al. (2024). High-temperature superconductivity with zero resistance and strange-metal behaviour in La3Ni2O7 −δ. Nat. Phys. 20: 1269−1273. DOI: 10.1038/s41567-024-02515-y. |
| [4] | Sakakibara, H., Ochi, M., Nagata, H., et al. (2024). Theoretical analysis on the possibility of superconductivity in the trilayer Ruddlesden-Popper nickelate La4Ni3O10 under pressure and its experimental examination: Comparison with La3Ni2O7. Phys. Rev. B 109: 144511. DOI: 10.1103/PhysRevB.109.144511. |
| [5] | Li, Q., Zhang, Y.-J., Xiang, Z.-N., et al. (2024). Signature of superconductivity in pressurized La4Ni3O10. Chin. Phys. Lett. 41: 017401. DOI: 10.1088/0256-307X/41/1/017401. |
| [6] | Zhu, Y., Peng, D., Zhang, E. et al. (2024). Superconductivity in pressurized trilayer La4Ni3O10 −δ single crystals. Nature 631: 531−536. DOI: 10.1038/s41586-024-07553-3. |
| [7] | Zhang, M., Pei, C., Du, X., et al. (2023). Superconductivity in trilayer nickelate La4Ni3O10 under pressure. arXiv:2311.07423. DOI: 10.48550/arXiv.2311.07423. |
| [8] | Li, J., Chen, C.-Q., Huang, C., et al. (2024). Structural transition, electric transport, and electronic structures in the compressed trilayer nickelate La4Ni3O10. Sci. China-Phys. Mech. Astron. 67: 117403. DOI: 10.1007/s11433-023-2329-x. |
| [9] | Liu, Z., Huo, M., Li, J. et al. (2024). Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7. Nat. Commun. 15: 7570. DOI: 10.1038/s41467-024-52001-5. |
| [10] | Yang, J., Sun, H., Hu, X. et al. (2024). Orbital-dependent electron correlation in double-layer nickelate La3Ni2O7. Nat. Commun. 15: 4373. DOI: 10.1038/s41467-024-48701-7. |
| [11] | Wang, G., Wang, N.-N., Shen, X.-L., et al. (2024). Pressure-induced superconductivity in polycrystalline La3Ni2O7 −δ. Phys. Rev. X 14: 011040. DOI: 10.1103/PhysRevX.14.011040. |
| [12] | Zhou, Y., Guo, J., Cai, S., et al. (2023). Evidence of filamentary superconductivity in pressurized La3Ni2O7. arXiv:2311.12361. DOI: 10.48550/arXiv.2311.12361. |
| [13] | Cui, T., Choi, S., Lin, T. et al. (2024). Strain-mediated phase crossover in Ruddlesden–Popper nickelates. Commun. Mater. 5: 32. DOI: 10.1038/s43246-024-00478-4. |
| [14] | Chen, K., Liu, X., Jiao, J., et al. (2024). Evidence of spin density waves in La3Ni2O7 −δ. Phys. Rev. Lett. 132: 256503. DOI: 10.1103/PhysRevLett.132.256503. |
| [15] | Dong, Z., Huo, M., Li, J. et al. (2024). Visualization of oxygen vacancies and self-doped ligand holes in La3Ni2O7 −δ. Nature 630: 847−852. DOI: 10.1038/s41586-024-07482-1. |
| [16] | Xie, T., Huo, M., Ni, X., et al. (2024). Neutron scattering studies on the high-Tc superconductor La3Ni2O7−δ at ambient pressure. arXiv:2401.12635. DOI: 10.48550/arXiv.2401.12635. |
| [17] | Chen, X., Choi, J., Jiang, Z., et al. (2024). Electronic and magnetic excitations in La3Ni2O7. arXiv:2401.12657. DOI: 10.48550/arXiv.2401.12657. |
| [18] | Dan, Z., Zhou, Y., Huo, M., et al. (2024). Spin-density-wave transition in double-layer nickelate La3Ni2O7. arXiv:2402.03952. DOI: 10.48550/arXiv.2402.03952. |
| [19] | Abadi, S. N., Xu, K. J., Lomeli, E. G., et al. (2024). Electronic structure of the alternating monolayer-trilayer phase of La3Ni2O7. arXiv:2402.07143. DOI: 10.48550/arXiv.2402.07143. |
| [20] | Yuan, N., Elghandour, A., Arneth, J., et al. (2024). High-pressure crystal growth and investigation of the metal-to-metal transition of Ruddlesden–Popper trilayer nickelates La4Ni3O10. J. Cryst. Growth 627: 127511. DOI: 10.1016/j.jcrysgro.2023.127511. |
| [21] | Kakoi, M., Oi, T., Ohshita, Y., et al. (2024). Multiband metallic ground state in multilayered nickelates La3Ni2O7 and La4Ni3O10 Probed by 139La-NMR at Ambient Pressure. J. Phys. Soc. Jpn. 93: 053702. DOI: 10.7566/JPSJ.93.053702. |
| [22] | Luo, Z., Hu, X., Wang, M., et al. (2023). Bilayer two-orbital model of La3Ni2O7 under pressure. Phys. Rev. Lett. 131: 126001. DOI: 10.1103/PhysRevLett.131.126001. |
| [23] | Zhang, Y., Lin, L.-F., Moreo, A., et al. (2023). Electronic structure, dimer physics, orbital-selective behavior, and magnetic tendencies in the bilayer nickelate superconductor La3Ni2O7 under pressure. Phys. Rev. B 108: L180510. DOI: 10.1103/PhysRevB.108.L180510. |
| [24] | Yang, Q.-G., Wang, D., and Wang, Q.-H. (2023). Possible s ±-wave superconductivity in La3Ni2O7. Phys. Rev. B 108: L140505. DOI: 10.1103/PhysRevB.108.L140505. |
| [25] | Lechermann, F., Gondolf, J., Bötzel, S., et al. (2023). Electronic correlations and superconducting instability in La3Ni2O7 under high pressure. Phys. Rev. B 108: L201121. DOI: 10.1103/PhysRevB.108.L201121. |
| [26] | Sakakibara, H., Kitamine, N., Ochi, M., et al. (2024). Possible high T c superconductivity in La3Ni2O7 under high pressure through manifestation of a nearly-half-filled bilayer Hubbard model. Phys. Rev. Lett. 132: 106002. DOI: 10.1103/PhysRevLett.132.106002. |
| [27] | Gu, Y., Le, C., Yang, Z., et al. (2023). Effective model and pairing tendency in bilayer Ni-based superconductor La3Ni2O7. arXiv:2306.07275. DOI: 10.48550/arXiv.2306.07275. |
| [28] | Shen, Y., Qin, M., and Zhang, G.-M. (2023). Effective bilayer model hamiltonian and density-matrix renormalization group study for the high-T c superconductivity in La3Ni2O7 under high pressure. Chin. Phys. Lett. 40: 127401. DOI: 10.1088/0256307X/40/12/127401. |
| [29] | Christiansson, V., Petocchi, F., and Werner, P. (2023). Correlated electronic structure of La3Ni2O7 under pressure. Phys. Rev. Lett. 131: 206501. DOI: 10.1103/PhysRevLett.131.206501. |
| [30] | Shilenko, D. A. and Leonov, I. V. (2023). Correlated electronic structure, orbital-selective behavior, and magnetic correlations in double-layer La3Ni2O7 under pressure. Phys. Rev. B 108: 125105. DOI: 10.1103/PhysRevB.108.125105. |
| [31] | Wú, W., Luo, Z., Yao, D.-X. et al. (2024). Charge transfer and Zhang-Rice singlet bands in the nickelate superconductor La3Ni2O7 under pressure. Sci. China-Phys. Mech. Astron. 67: 117402. DOI: 10.1007/s11433-023-2300-4. |
| [32] | Cao, Y. and Yang, Y.-F. (2024). Flat bands promoted by Hund’s rule coupling in the candidate double-layer high-temperature superconductor La3Ni2O7. Phys. Rev. B 109: L081105. DOI: 10.1103/PhysRevB.109.L081105. |
| [33] | Chen, X., Jiang, P., Li, J., et al. (2023). Critical charge and spin instabilities in superconducting La3Ni2O7. arXiv:2307.07154. DOI: 10.48550/arXiv.2307.07154. |
| [34] | Liu, Y.-B., Mei, J.-W., Ye, F., et al. (2023). s ±-Wave pairing and the destructive role of apical-oxygen deficiencies in La3Ni2O7 under pressure. Phys. Rev. Lett. 131: 236002. DOI: 10.1103/PhysRevLett.131.236002. |
| [35] | Lu, C., Pan, Z., Yang, F., et al. (2024). Interlayer coupling driven high-temperature superconductivity in La3Ni2O7 under pressure. Phys. Rev. Lett. 132: 146002. DOI: 10.1103/PhysRevLett.132.146002. |
| [36] | Zhang, Y., Lin, L.-F., Moreo, A. et al. (2024). Structural phase transition, s ±-wave pairing and magnetic stripe order in the bilayered nickelate superconductor La3Ni2O7 under pressure. Nat. Commun. 15: 2470. DOI: 10.1038/s41467-024-46622-z. |
| [37] | Oh, H. and Zhang, Y.-H. (2023). Type-II t-J model and shared superexchange coupling from Hund’s rule in superconducting La3Ni2O7. Phys. Rev. B 108: 174511. DOI: 10.1103/PhysRevB.108.174511. |
| [38] | Liao, Z., Chen, L., Duan, G., et al. (2023). Electron correlations and superconductivity in La3Ni2O7 under pressure tuning. Phys. Rev. B 108: 214522. DOI: 10.1103/PhysRevB.108.214522. |
| [39] | Qu, X.-Z., Qu, D.-W., Chen, J., et al. (2024). Bilayer t-J-J⊥ model and magnetically mediated pairing in the pressurized nickelate La3Ni2O7. Phys. Rev. Lett. 132: 036502. DOI: 10.1103/PhysRevLett.132.036502. |
| [40] | Yang, Y.-F., Zhang, G.-M., and Zhang, F.-C. (2023). Interlayer valence bonds and two-component theory for high-T c superconductivity of La3Ni2O7 under pressure. Phys. Rev. B 108: L201108. DOI: 10.1103/PhysRevB.108.L201108. |
| [41] | Jiang, K., Wang, Z., and Zhang, F.-C. (2024). High-temperature superconductivity in La3Ni2O7. Chin. Phys. Lett. 41: 017402. DOI: 10.1088/0256-307X/41/1/017402. |
| [42] | Zhang, Y., Lin, L.-F., Moreo, A., et al. (2023). Trends in electronic structures and s ±-wave pairing for the rare-earth series in bilayer nickelate superconductor R3Ni2O7. Phys. Rev. B 108: 165141. DOI: 10.1103/PhysRevB.108.165141. |
| [43] | Huang, J., Wang, Z.-D., and Zhou, T. (2023). Impurity and vortex states in the bilayer high-temperature superconductor La3Ni2O7. Phys. Rev. B 108: 174501. DOI: 10.1103/PhysRevB.108.174501. |
| [44] | Qin, Q. and Yang, Y.-F. (2023). High-T c superconductivity by mobilizing local spin singlets and possible route to higher T c in pressurized La3Ni2O7. Phys. Rev. B 108: L140504. DOI: 10.1103/PhysRevB.108.L140504. |
| [45] | Tian, Y.-H., Chen, Y., Wang, J.-M., et al. (2024). Correlation effects and concomitant two-orbital s ±-wave superconductivity in La3Ni2O7 under high pressure. Phys. Rev. B 109: 165154. DOI: 10.1103/PhysRevB.109.165154. |
| [46] | Luo, Z., Lv, B., Wang, M., (2024). High Tc superconductivity in La3Ni2O7 based on the bilayer two-orbital t-J model. Npj Quantum Mater. 9 : 61. DOI: 10.1038/s41535-024- 00668-w. |
| [47] | Zhang, J.-X., Zhang, H.-K., You, Y.-Z., et al. (2024). Strong pairing originated from an emergent Z2 Berry phase in La3Ni2O7. Phys. Rev. Lett. 133 : 126501 (2024). DOI: 10.1103/PhysRevLett.133.126501. |
| [48] | Geisler, B., Hamlin, J. J., Stewart, G. R., et al. (2024). Structural transitions, octahedral rotations, and electronic properties of A3Ni2O7 rare-earth nickelates under high pressure. Npj Quantum Mater. 9: 38. DOI: 10.1038/s41535-024-00648-0. |
| [49] | Kaneko, T., Sakakibara, H., Ochi, M., et al. (2024). Pair correlations in the two-orbital Hubbard ladder: Implications for superconductivity in the bilayer nickelate La3Ni2O7. Phys. Rev. B 109: 045154. DOI: 10.1103/PhysRevB.109.045154. |
| [50] | Lu, C., Pan, Z., Yang, F., et al. (2024). Interplay of two E g orbitals in superconducting La3Ni2O7 under pressure. Phys. Rev. B 110: 094509. DOI: 10.1103/PhysRevB.110.094509. |
| [51] | Ryee, S., Witt, N., and Wehling, T. O. (2024). Quenched pair breaking by interlayer correlations as a key to superconductivity La3Ni2O7. Phys. Rev. Lett. 133: 096002. DOI: 10.1103/PhysRevLett.133.096002. |
| [52] | Chen, J., Yang, F., and Li, W. (2024). Orbital-selective superconductivity in the pressurized bilayer nickelate La3Ni2O7: An infinite projected entangled-pair state study. Phys. Rev. B 110: L041111. DOI: 10.1103/PhysRevB.110.L041111. |
| [53] | Liu, H., Xia, C., Zhou, S., et al. (2023). Role of crystal-field-splitting and long-range-hoppings on superconducting pairing symmetry of La3Ni2O7. arXiv:2311.07316. DOI: 10.48550/arXiv.2311.07316. |
| [54] | Wang, L., Li, Y., Xie, S., et al. (2023). Structure responsible for the superconducting state in La3Ni2O7 at high pressure and low temperature conditions. arXiv:2311.09186. DOI: 10.48550/arXiv.2311.09186. |
| [55] | Chang, W.-X., Guo, S., You, Y.-Z. et al. (2023). Fermi surface symmetric mass generation: a quantum Monte-Carlo study. arXiv:2311.09970. DOI: 10.48550/arXiv.2311.09970. |
| [56] | Ouyang, Z., Wang, J.-M., Wang, J.-X., et al. (2024). Hund electronic correlation in La3Ni2O7 under high pressure. Phys. Rev. B 109: 115114. DOI: 10.1103/PhysRevB.109.115114. |
| [57] | Qu, X.-Z., Qu, D.-W., Li, W., et al. (2023). Roles of Hund’s rule and hybridization in the two-orbital model for high-Tc superconductivity in the bilayer nickelate. arXiv:2311.12769. DOI: 10.48550/arXiv.2311.12769. |
| [58] | Zheng, Y.-Y. and Wu, W. (2023). Superconductivity in the bilayer two-orbital Hubbard model. arXiv:2312.03605. DOI: 10.48550/arXiv.2312.03605. |
| [59] | Heier, G., Park, K., and Savrasov, S. Y. (2024). Competing d xy and s ± pairing symmetries in superconducting La3Ni2O7 emerge from LDA+FLEX calculations. Phys. Rev. B 109: 104508. DOI: 10.1103/PhysRevB.109.104508. |
| [60] | Fan, Z., Zhang, J.-F., Zhan, B., et al. (2024). Superconductivity in nickelate and cuprate superconductors with strong bilayer coupling. Phys. Rev. B 110: 024514. DOI: 10.1103/PhysRevB.110.024514. |
| [61] | Talantsev, E. F., and Chistyakov, V. V. (2024). Debye temperature, electron-phonon coupling constant, and microcrystalline strain in highly-compressed La3Ni2O7−δ. Lett. on Mater. 14 : 262-268 (2024). DOI: 10.48612/letters/2024-3-262-268. |
| [62] | Wang, Y., Jiang, K., Wang, Z., et al. (2024). Electronic structure and superconductivity in bilayer La3Ni2O7. arXiv:2401.15097. DOI: 10.48550/arXiv.2401.15097. |
| [63] | Bötzel, S., Lechermann, F., Gondolf, J., et al. (2024). Theory of magnetic excitations in multilayer nickelate superconductor La3Ni2O7. Phys. Rev. B 109: L180502. DOI: 10.1103/PhysRevB.109.L180502. |
| [64] | Xue, J.-R., and Wang, F. (2024). Magnetism and superconductivity in the t-J model of La3Ni2O7 under multiband gutzwiller approximation. Chin. Phys. Lett. 41: 05740. DOI: 10.1088/0256-307X/41/5/057403. |
| [65] | Leonov, I. V. (2024). Electronic structure and magnetic correlations in trilayer nickelate superconductor La4Ni3O10 under pressure. Phys. Rev. B 109: 235123. DOI: 10.1103/PhysRevB.109.235123. |
| [66] | Tian, P.-F., Ma, H.-T., Ming, X., et al. (2024). Effective model and electron correlations in trilayer nickelate superconductor La4Ni3O10. J. Phys: Condens. Matter 36: 355602. DOI: 10.1088/1361-648X/ad512c. |
| [67] | Wang, J.-X., Ouyang, Z., He, R.-Q., et al. (2024). Non-Fermi liquid and Hund correlation in La4Ni3O10 under high pressure. Phys. Rev. B 109: 165140. DOI: 10.1103/PhysRevB.109.165140. |
| [68] | LaBollita, H., Kapeghian, J., Norman, M. R., et al. (2024). Electronic structure and magnetic tendencies of trilayer La4Ni3O10 under pressure: Structural transition, molecular orbitals, and layer differentiation. Phys. Rev. B 109: 195151. DOI: 10.1103/PhysRevB.109.195151. |
| [69] | Zhang, Y., Lin, L. F., Moreo, A., et al. (2024). Prediction of s ±-wave superconductivity enhanced by electronic doping in trilayer nickelates La4Ni3O10 under pressure. Phys. Rev. Lett. 133: 136001. DOI: 10.1103/PhysRevLett.133.136001. |
| [70] | Yang, Q. G., Jiang, K. Y., Wang, D., et al. (2024). Effective model and s ±-wave superconductivity in trilayer nickelate La4Ni3O10. Phys. Rev. B 109: L220506. DOI: 10.1103/PhysRevB.109.L220506. |
| [71] | Lu, C., Pan, Z., Yang, F., et al. (2024). Superconductivity in La4Ni3O10 under pressure. arXiv:2402.06450. DOI: 10.48550/arXiv.2402.06450. |
| [72] | Luo, Z., Chen, C.-Q., Wang, M., et al. (2024). Trilayer multi-orbital models of La4Ni3O10. Phys. Rev. B 110: 014503. DOI: 10.1103/PhysRevB.110.014503. |
| [73] | Zhang, M., Sun, H., Liu, Y. B., et al. (2024). The s±-wave superconductivity in the pressurized La4Ni3O10. arXiv:2402.07902. DOI: 10.48550/arXiv.2402.07902. |
| [74] | Scalapino, D. J. (2012). A common thread: The pairing interaction for unconventional superconductors. Rev. Mod. Phys. 84: 1383. DOI: 10.1103/RevModPhys.84.1383. |
| [75] | Wang, Z., Zou, C., Lin, C., et al. (2023). Correlating the charge-transfer gap to the maximum transition temperature in Bi2Sr2Ca n−1Cu nO2 n+4 δ. Science 381: 227−231. DOI: 10.1126/science.add3672. |
| [76] | Li, H., Zhou, X., Nummy, T., et al. (2017). Fermiology and electron dynamics of trilayer nickelate La4Ni3O10. Nat. Commun. 8: 704. DOI: 10.1038/s41467-017-00777-0. |
| [77] | Mayr, M., Alvarez, G., S¸en, C., et al. (2005). Phase fluctuations in strongly coupled d-wave superconductors. Phys. Rev. Lett. 94: 217001. DOI: 10.1103/PhysRevLett.94.217001. |
| [78] | Dubi, Y., Meir, Y. and Avishai, Y. (2007). Nature of the superconductor-insulator transition in disordered superconductors. Nature 449: 876−880. DOI: 10.1038/nature06180. |
| [79] | Karmakar, M. (2020). Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions. J. Phys.: Condens. Matter 32: 405604. DOI: 10.1088/1361648X/ab926a. |
| [80] | Pasrija, K., Chakraborty, P. B., and Kumar, S. (2016). Effective Hamiltonian based Monte Carlo for the BCS to BEC crossover in the attractive Hubbard model. Phys. Rev. B 94: 165150. DOI: 10.1103/PhysRevB.94.165150. |
| [81] | Dong, J.-J., Huang, D., and Yang, Y.-F. (2021). Mutual information, quantum phase transition, and phase coherence in Kondo systems. Phys. Rev. B 104: L081115. DOI: 10.1103/PhysRevB.104.L081115. |
| [82] | Dong, J.-J. and Yang, Y.-F. (2022). Development of long-range phase coherence on the Kondo lattice. Phys. Rev. B 106: L161114. DOI: 10.1103/PhysRevB.106.L161114. |
| [83] | Mukherjee, A., Patel, N. D., Dong, S., et al. (2014). Testing the Monte Carlo-mean field approximation in the one-band Hubbard model. Phys. Rev. B 90: 205113. DOI: 10.1103/PhysRevB.90.205133. |
| [84] | Liang, S., Moreo, A., and Dagotto, E. (2013). Nematic state of pnictides stabilized by interplay between spin, orbital, and lattice degrees of freedom. Phys. Rev. Lett. 111: 047004. DOI: 10.1103/PhysRevLett.111.047004. |
| [85] | Qin, Q., Dong, J.-J., Sheng, Y., Huang, D., et al. (2023). Superconducting fluctuations and charge-4e plaquette state at strong coupling. Phys. Rev. B 108: 054506. DOI: 10.1103/PhysRevB.108.054506. |
| [86] | Han, Q., Li, T., and Wang, Z. D. (2010). Pseudogap and Fermi-arc evolution in the phase-fluctuation scenario. Phys. Rev. B 82: 052503. DOI: 10.1103/PhysRevB.82.052503. |
| [87] | Zhong, Y. W., Li, T., and Han, Q. (2011). Monte Carlo Study of thermal fluctuations and Fermi-arc formation in d-wave superconductors. Phys. Rev. B 84: 024522. DOI: 10.1103/PhysRevB.84.024522. |
| [88] | Singh, D. K., Kadge, S., Bang, Y., et al. (2022). Fermi arcs and pseudogap phase in a minimal microscopic model of d-wave superconductivity. Phys. Rev. B 105: 054501. DOI: 10.1103/PhysRevB.105.054501. |
| [89] | Coleman, P. (2015). Introduction to many-body physics. (Cambridge University Press). |
| [90] | Berezinskii, V. L. (1972). Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum Systems. Sov. Phys. JETP 34: 610. |
| [91] | Kosterlitz, J. M. and Thouless, D. J. (1973). Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6: 1181. DOI: 10.1088/0022-3719/6/7/010. |
| [92] | Kosterlitz, J. M. (1974). The critical properties of the two-dimensional XY model. J. Phys. C 7: 1046. DOI: 10.1088/0022-3719/7/6/005. |
| [93] | Drouin-Touchette, V. The Kosterlitz-Thouless phase transition: An introduction for the intrepid student. arXiv:2207.13748. DOI:10.48550/arXiv.2207.13748. |
| [94] | Cover, T. M. and Thomas, J. A. (2006). Elements of information theory. (Wiley Series in Telecommunications and Signal Processing). |
| [95] | Kraskov, A., Stögbauer, H., and Grassberger, P. (2004). Estimating mutual information. Phys. Rev. E 69: 066138. DOI: 10.1103/PhysRevE.69.066138. |
| [96] | Darbellay, G. A., and Vajda, I. (1999). Estimation of the information by an adaptive partitioning of the observation space. IEEE Trans. Inf. Theory 45: 1315−1321. DOI: 10.1109/18.761290. |
| [97] | Khan, S., Bandyopadhyay, S., Ganguly, A. R., et al. (2007). Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data. Phys. Rev. E 76: 026209. DOI: 10.1103/PhysRevE.76.026209. |
| [98] | Belghazi, M. I., Baratin, A., Rajeshwar, S., et al. (2018). Mutual information neural estimation. Dy, J. and Krause, A. (eds). Proceedings of the 35th international conference on machine learning, pp: 531. |
| [99] | Poole, B., Ozair, S., Van Den Oord, A., et al. (2019). On variational bounds of mutual information. Chaudhuri, K. and Salakhutdinov, R. (eds). Proceedings of the 36th international conference on machine learning, pp: 5171. |
| [100] | Le Tacon, M., Ghiringhelli, G., Chaloupka, J. et al. (2011). Intense paramagnon excitations in a large family of high-temperature superconductors. Nat. Phys. 7: 725. DOI: 10.1038/nphys2041. |
| [101] | Keimer, B., Kivelson, S., Norman, M. et al. (2015). From quantum matter to high-temperature superconductivity in copper oxides. Nature 518: 179−186. DOI: 10.1038/nature14165. |
| [102] | Emery, V. and Kivelson, S. (1995). Importance of phase fluctuations in superconductors with small superfluid density. Nature 374: 434−437. DOI: 10.1038/374434a0. |
| [103] | Qin, Q. and Yang, Y.-F. (2024). Intrinsic constraint on Tc for unconventional superconductivity. arXiv:2402.07128. DOI: 10.48550/arXiv.2402.07128. |
| [104] | Chen, X., Zhang, J., Thind, A. S., et al. (2024). Polymorphism in Ruddlesden-Popper La3Ni2O7: Discovery of a hidden phase with distinctive layer stacking. J. Am. Chem. Soc. 146: 3640−3645. DOI: 10.1021/jacs.3c14052. |
| [105] | Puphal, P., Reiss, P., Enderlein, N., et al. (2023). Unconventional crystal structure of the high-pressure superconductor La3Ni2O7. arXiv:2312.07341. DOI: 10.48550/arXiv.2312.07341. |
| [106] | Wang, H., Chen, L., Rutherford, A., et al. (2024). Long-range structural order in a hidden phase of Ruddlesden-Popper bilayer nickelates La3Ni2O7. Inorg. Chem. 63: 5020−5026. DOI: 10.1021/acs.inorgchem.3c04474. |
| [107] | Li, J., Ma, P., Zhang, H., et al. (2024). Pressure-driven right-triangle shape superconductivity in bilayer nickelate La3Ni2O7. arXiv:2404.11369. DOI: 10.48550/arXiv.2404.11369. |
| Qin Q., Wang J., and Yang Y (2024). Frustrated superconductivity and intrinsic reduction of Tc in trilayer nickelate. The Innovation Materials 2(4): 100102. https://doi.org/10.59717/j.xinn-mater.2024.100102 |
To request copyright permission to republish or share portions of our works, please visit Copyright Clearance Center's (CCC) Marketplace website at marketplace.copyright.com.
Superconducting transition temperature
Interlayer superconducting fluctuations
Effect of the interlayer hopping
Superconducting gap structures