Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level

TL;DR

This paper reveals that the flat bands in twisted bilayer graphene can be understood as Landau levels in an external magnetic field, uncovering a hidden wave function solution with implications for additional flat bands.

Contribution

It introduces a novel interpretation of flat bands as Landau levels and identifies a hidden wave function solution with a pole in the continuum model of twisted bilayer graphene.

Findings

Flat bands can be viewed as Landau levels in an external magnetic field.

A hidden wave function with a pole exists in the model.

Extra flat bands are predicted in the presence of a magnetic field.

Abstract

We study the chirally symmetric continuum model (CS-CM) of the twisted bilayer graphene. The equation on a flat band could be interpreted as a Dirac equation on a torus in the external non-abelian magnetic field. We prove that the existence of the flat band implies that the wave-function has a zero and vice verse. We found a hidden solution in the CS-CM model that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.