Variational Quantum Monte Carlo investigations of the superconducting pairing in La$_3$Ni$_2$O$_7$

TL;DR

This study uses variational quantum Monte Carlo to explore the pairing symmetry in La$_3$Ni$_2$O$_7$, revealing an $s_$-wave pairing driven by strong correlations, with the 3d$_{3z^2-r^2}$ orbital playing a key role.

Contribution

It introduces a non-perturbative quantum Monte Carlo approach to identify the dominant $s_$-wave pairing in La$_3$Ni$_2$O$_7$ and highlights the importance of the 3d$_{3z^2-r^2}$ orbital.

Findings

$s_$-wave pairing with sign change among Fermi pockets

The 3d$_{3z^2-r^2}$ orbital is crucial for pairing

Finite intra-orbital double occupancy persists in strong correlations

Abstract

We investigate the pairing symmetry in the novel superconductor La$_3$Ni$_2$O$_7$ under pressure by the non-perturbative variational quantum Monte Carlo. Within the bilayer Hubbard model and extended $t-J$ model with two orbitals in the $E_g$ doublet, we find the local strong correlation triggers $s_\pm$-wave Cooper pairing, with sign change of the gap function among the various Fermi pockets, while the $d_{x^2-y^2}$-wave pairing is generically disfavored. This is in agreement with the results from functional renormalization group applied in the weak up to moderate correlation limit. We find the 3d$_{3z^2-r^2}$ orbital plays a leading role in the superconducting pairing. We also demonstrate the finite intra-orbital double occupancy even in the strong correlation limit, shedding light on the itinerant versus local moment picture of the electrons in this material.