Efficient prediction of superlattice and anomalous miniband topology from quantum geometry

TL;DR

This paper introduces a fast, versatile method combining perturbation theory and symmetry indicators to predict topological properties of superlattice-induced minibands in 2D materials, including interaction effects.

Contribution

It develops a new computational approach to determine topological invariants in superlattice-modulated materials, applicable to both non-interacting and interaction-generated bands.

Findings

Provides a systematic rule for Chern number calculation in superlattice minibands.

Derives an efficient algorithm for Chern numbers in interaction-induced bands.

Offers microscopic insight into quantum anomalous Hall insulators in rhombohedral graphene.

Abstract

Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.