Spin density wave and superconductivity in the bilayer $t$-$J$ model of $\rm{La}_{3}Ni_{2}O_{7}$ under renormalized mean-field theory

TL;DR

This paper develops a renormalized mean-field theory for a bilayer $t$-$J$ model of $ m{La}_{3}Ni_{2}O_{7}$, revealing how magnetism and superconductivity coexist and transition with doping and interlayer interactions, aligning with experimental observations.

Contribution

It introduces a theoretical framework for the interplay of magnetism and superconductivity in bilayer nickelates, predicting pairing symmetry changes and magnetic order transitions under doping and interlayer coupling.

Findings

Magnetic order is suppressed with increased hole doping.

Transition from $d$-wave to $s$-wave pairing occurs with stronger interlayer coupling.

Coexistence of spin density waves and superconductivity is predicted.

Abstract

Motivated by the recently discovered bilayer nickelate superconductor, the pressurized $\rm{La}_{3}Ni_{2}O_{7}$, we present a renormalized mean-field theory of a bilayer single-band $t$-$J$ model, highlighting the interplay between magnetism and superconductivity. We analyze the pairing symmetry and magnetic properties of the system, predicting two distinct states in which magnetism and superconductivity coexist. As hole doping increases, the magnetic order is rapidly suppressed. The inter-layer hopping $t_{\perp}$ and coupling $J_{\perp}$ promote a transition from intra-layer $d$-wave pairing to $s$-wave pairing, which is accompanied by a shift from antiferromagnetic (AFM) order to a double spin stripe configuration. The latter has been extensively observed in ambient and high-pressure experiments. Our study offers theoretical insights into the coexistence of spin density waves and superconductivity.