Anderson's theorem for correlated insulating states in twisted bilayer graphene

TL;DR

This paper derives an Anderson theorem showing the robustness of the K-IVC state in twisted bilayer graphene against certain types of disorder, explaining its stability and sample dependence of correlated insulating phases.

Contribution

It introduces an Anderson theorem for the K-IVC state, identifying conditions under which it remains robust against disorder in twisted bilayer graphene.

Findings

K-IVC gap is robust against $ ext{PT}$-odd perturbations

$ ext{PT}$-even perturbations can induce subgap states

The theorem classifies stability of the K-IVC state under disorder

Abstract

The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moir\'e flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under $\mathcal{PT}$, where $\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time reversal, respectively. In contrast, $\mathcal{PT}$-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states.