Landau Levels as a Probe for Band Topology in Graphene Moir\'e Superlattices

TL;DR

This paper demonstrates that Landau level spectra in twisted bilayer graphene can reveal the topological nature of electronic bands, providing a new experimental probe for valley Chern numbers in moiré superlattices.

Contribution

It introduces Landau levels as a method to distinguish topological differences in flat bands of twisted double bilayer graphene configurations.

Findings

Different Landau level sequences for AB-AB and AB-BA configurations.

Landau level sequences linked to orbital magnetization distribution.

Hofstadter spectra can detect non-trivial valley band topology.

Abstract

We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moir\'e superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational $C_2$ and time-reversal $\mathcal{T}$ symmetries. Our results can be readily extended to other twisted graphene multilayers and $h$-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the non-trivial valley band topology.