The $s\pm$ pairing symmetry in the pressured La$_3$Ni$_2$O$_7$ from electron-phonon coupling

Abstract

The recently discovered bilayer Ruddlesden-Popper nickelate La$_3$Ni$_2$O$_7$ exhibits superconductivity with a remarkable transition temperature $T_c\approx 80 $ K under applied pressures above 14.0 GPa. This discovery of new family of high-temperature superconductors has garnered significant attention in the condensed matter physics community. In this work, we assume the this high-temperature superconductor is mediated by phonons and investigate the pairing symmetry in two distinct models: (i) the full-coupling case, where the Ni-$d_{x^2-y^2}$ and Ni-$d_{3z^2-r^2}$ orbitals are treated equally in both interlayer and intralayer coupling interactions, and (ii) the half-coupling case, where the intralayer coupling involves only the $d_{x^2-y^2}$ orbital, while the interlayer coupling is restricted to the $d_{3z^2-r^2}$ orbital. Our calculations reveal that the interlayer coupling favors an $s\pm$-wave superconducting state, whereas the intralayer coupling promotes an $s++$-wave symmetry. Additionally, we discuss the implications of pair-hopping interactions on the superconducting properties. These findings provide valuable insights into the pairing mechanisms and symmetry of this newly discovered high-temperature superconductor.

Figures (10)

• Figure 1: The orbital-weight band structureluo2023bilayer (a) and Fermi surfaces (b-d) of the bilayer tight-binding model in the pressured LNO. (b) labels the Fermi surface with $\mu=-0.328eV$ where it manifest a van Hove singularity. (c) and (d) illustrates the Fermi surface with $\mu=0eV$ and $0.1eV$, respectively.
• Figure 2: The pairing gap in the full-coupling case with different parameters. (a), (b) and (c) illustrates the numerical result with only intralayer coupling $g_2^f=0.12$ for $\mu=-0.328eV$, $0eV$ and $0.1eV$ respectively. (d), (e) and (f) illustrates the numerical result with only interlayer coupling $g_1^f=0.12$ for $\mu=-0.328eV$, $0eV$ and $0.1eV$ respectively.
• Figure 3: (a)The momentum distribution at Fermi surfaces when calculating effective interacting strength with fixed $\mu=0eV$. Effective interacting strength $g^{\alpha\alpha}$ (b), $g^{\alpha\gamma}$ (c) and $g^{\alpha\beta}$ (d) obtained in the full-coupling case with the pure interlayer coupling $g_2^f=0.12$. Effective interacting strength $g^{\alpha\gamma}$ (e) and $g^{\alpha\beta}$ (f) obtained in the full-coupling case with the pure intralayer coupling $g_1^f=0.06$.
• Figure 4: The pairing gap with fixed interlayer coupling $g_2^f=0.12$ while varying intralayer coupling $g_1^f=0.006$ (a) and $0.072$ (b) in the full-coupling case with chemical potential $\mu=0$.
• Figure 5: The pairing gap in the half-coupling case with different parameters. (a), (b) and (c) illustrates the numerical result with only intralayer coupling $g_1^f=0.18$ for $\mu=-0.328eV$, $0eV$ and $0.1eV$ respectively. (d), (e) and (f) illustrates the numerical result with only interlayer coupling $g_2^f=0.18$ for $\mu=-0.328eV$, $0eV$ and $0.1eV$ respectively.