How a bilayer Nickelate superconducts: a Quantum Monte Carlo study

TL;DR

This study uses determinant Quantum Monte Carlo to explore how doping, inter-layer tunneling, and Hund's coupling influence superconductivity in a bilayer Nickelate model, revealing key symmetries and competing phases.

Contribution

It demonstrates the absence of a sign problem in a realistic bilayer Nickelate model and uncovers the interplay between superconductivity and exciton condensation, highlighting the role of inter-layer tunneling.

Findings

Superconductivity is stabilized under certain interaction parameters.

A second instability towards exciton condensation is identified.

Inter-layer tunneling critically influences the competition between phases.

Abstract

Using determinant Quantum Monte Carlo, we investigate the interplay between doping, inter-layer tunneling and onsite Hund's coupling in stabilizing superconductivity (SC) in a two-orbital model for the bilayer Nickelate $\text{La}_3\text{Ni}_2\text{O}_7$. With realistic dispersion and for certain values of the interaction parameters, the auxiliary-field-decoupled fermion Hamiltonian has Kramers anti-unitary symmetries which guarantee the absence of a sign problem. The same anti-unitary symmetries can also be used to show there is a second instability towards $(\pi,\pi)$ exciton condensation in the strong interaction limit. We indicate the possible connection between this exciton order and the enigmatic density wave state observed in experiment, and clarify the decisive role played by the inter-layer tunneling in the competition between SC and exciton condensation. Finally, possible directions on how to enhance the SC transition temperature and stabilize the SC phase are also discussed.