Moir\'e disorder effect in twisted bilayer graphene

TL;DR

This paper investigates how disordered moiré patterns and heterostrain affect the electronic structure of magic-angle twisted bilayer graphene, revealing that local vector potentials primarily determine the flat band splitting.

Contribution

The study introduces an extended continuum model that incorporates non-uniform lattice distortions to analyze disorder effects in twisted bilayer graphene.

Findings

Local density of states remains sharp despite disorder.

Splitting of flat bands is mainly governed by local vector potentials.

Analytic expression for splitting energy as a function of strain amplitude.

Abstract

We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moir\'e patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moir\'e period give relatively minor effects on the electronic structure. We explain the exclusive dependence on the local vector potential by a pseudo Landau level picture for the magic-angle flat band, and we obtain an analytic expression of the splitting energy as a function of the strain amplitude.