| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-$T_{\rm c}$ Superconductivity in La$_{3}$Ni$_{2}$O$_{7}$ under High Pressure |
| Yang Shen1, Mingpu Qin1,2*, and Guang-Ming Zhang3,4* |
1Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
2Hefei National Laboratory, Hefei 230088, China
3State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
4Frontier Science Center for Quantum Information, Beijing 100084, China
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| Cite this article: |
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Yang Shen, Mingpu Qin, and Guang-Ming Zhang 2023 Chin. Phys. Lett. 40 127401 |
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Abstract High-$T_{\rm c}$ superconductivity with possible $T_{\rm c}\approx 80$ K has been reported in the single crystal of ${\rm La}_{3}{\rm Ni}_{2}{\rm O}_{7}$ under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbital electrons of the nickel cations. The main feature of the model is that the $3d_{z^{2}}$ electrons form inter-layer $\sigma$-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the $3d_{x^{2}-y^{2}}$ electrons hybridize with the $3d_{z^{2}}$ electrons within each NiO$_2$ plane. The chemical potential difference of these two orbital electrons ensures that the $3d_{z^{2}}$ orbitals are close to half-filling and the $3d_{x^{2}-y^{2}}$ orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the $3d_{z^{2}}$ orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange $J$. Applying pressure can self dope holes on the $3d_{z^{2}}$ orbitals with the same amount of electrons doped on the $3d_{x^{2}-y^{2}}$ orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large $J$ and small doping of $3d_{z^{2}}$ orbitals, we find the superconducting instability on both the $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-$T_{\rm c}$ superconductivity in single crystal La$_3$Ni$_2$O$_7$ under high pressure.
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Received: 02 November 2023
Express Letter
Published: 21 November 2023
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| PACS: |
74.70.-b
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(Superconducting materials other than cuprates)
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74.90.+n
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(Other topics in superconductivity)
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