Simulating superconductivity in mixed-dimensional $t_\parallel$-${J}_\parallel$-${J}_\perp$ bilayers with neural quantum states

TL;DR

This paper uses neural quantum states to simulate a bilayer model inspired by nickelate superconductors, revealing diverse pairing behaviors and phase transitions, and providing the first high-precision numerical evidence of superconductivity in such systems.

Contribution

First application of neural quantum states to simulate a fermionic multi-orbital bilayer system, demonstrating superconductivity and pairing transitions with high accuracy.

Findings

Superconductivity observed across various dopings and couplings.

Crossover from Bose-Einstein to BCS-like pairs with changing interlayer exchange.

Transition from interlayer s-wave to intralayer d-wave pairing.

Abstract

Motivated by the recent discovery of superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer $t_\parallel$-$J_\parallel$-$J_\perp$ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to $8\times 8\times 2$ sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer $s$-wave pairing to intralayer $d$-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.