Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators

TL;DR

This paper demonstrates that flat bands in chiral twisted bilayer graphene remain exactly flat under a magnetic field, enabling analysis of fractional Chern insulators and revealing a topological phase transition at one flux quantum per unit cell.

Contribution

It provides an exact mapping between the flat bands and Landau level wavefunctions, revealing a topological phase transition and enabling study of fractional Chern insulators in this system.

Findings

Flat bands remain exactly flat in a magnetic field.

An exact mapping to Landau level wavefunctions is established.

A topological phase transition occurs at one flux quantum per unit cell.

Abstract

We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field.