Incipient quantum spin Hall insulator under strong correlations

TL;DR

This study uses non-perturbative quantum Monte Carlo simulations to show that the Kane-Mele-Hubbard model under strong correlations favors a quantum spin Hall insulator state over a proposed antiferromagnetic Chern insulator, clarifying the nature of topological phases.

Contribution

It provides non-perturbative evidence that the low-temperature phase is a quantum spin Hall insulator, challenging prior mean-field predictions of a $z$-antiferromagnetic Chern insulator in the Kane-Mele-Hubbard model.

Findings

Quantum spin Hall insulator is stabilized at intermediate sub-lattice potential and high on-site repulsion.

$xy$-antiferromagnetic fluctuations dominate at low temperature, suppressing $z$-AFM Chern insulator.

Results align with experimental observations of quantum spin Hall effects in twisted bilayer TMDs.

Abstract

To assess prior mean-field claims that the interacting Kane-Mele model hosts a novel $z-$antiferromagnetic (AFM) Chern insulating phase for a wide range of sub-lattice potentials, we analyze the Kane-Mele-Hubbard model in the presence of a sub-lattice potential using non-perturbative determinant quantum Monte Carlo simulations. We find instead that the true low-temperature state is a quantum spin Hall insulator for intermediate values of the sub-lattice potential $\lambda_v$ and large on-site repulsion. Two kinds of magnetic fluctuations are found to compete: $z$- and $xy$-AFM. The latter dominates at low temperature leading to a stabilization of the quantum spin Hall state as opposed to $z-$AFM Chern insulator. Our work is consistent with the robust quantum spin Hall effects which are consistently observed at even-integer fillings over a wide range of parameters in twisted bilayer MoTe$_2$ and WSe$_2$ as well as AB stacked MoTe$_2$/WSe$_2$.