Magic angle (in)stability and mobility edges in disordered Chern insulators

TL;DR

This paper investigates the stability and transport properties of magic angles in disordered Chern insulators, revealing persistent mobility edges and topological features that explain experimental observations in twisted bilayer graphene.

Contribution

It analyzes the impact of disorder on magic angles and topological transport, highlighting the robustness of mobility edges and $C_{2z}T$ symmetry effects beyond the chiral limit.

Findings

Mobility edge persists near flat band energy despite zero Chern numbers.

$C_{2z}T$ symmetry enables non-trivial sublattice transport.

Robustness of effects beyond the chiral limit and near perfect magic angles.

Abstract

Why do experiments only observe one magic angle in twisted bilayer graphene, despite standard models like the chiral limit of the Bistritzer-MacDonald Hamiltonian predicting an infinite number? In this article, we explore the relative stability of larger magic angles compared to smaller ones. Specifically, we analyze how disorder impacts these angles as described by the Bistritzer-MacDonald Hamiltonian in the chiral limit. Changing focus, we investigate the topological and transport properties of a specific magic angle under disorder. We identify a mobility edge near the flat band energy for small disorder, showing that this mobility edge persists even when all Chern numbers are zero. This persistence is attributed to the system's $C_{2z}T$ symmetry, which enables non-trivial sublattice transport. Notably, this effect remains robust beyond the chiral limit and near perfect magic angles, aligning with experimental observations.