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

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.