An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

TL;DR

This paper introduces a novel curved space-time geometric theory for twisted bilayer graphene, accurately reproducing flat bands and enabling predictions for rotating configurations beyond previous models.

Contribution

It develops a geometric formalism based on curved space-time Dirac theory that captures flat bands and predicts properties of rotating bilayer graphene not accessible by earlier theories.

Findings

Reproduces nearly flat bands around the first magic angle

Predicts properties of rotating bilayer graphene, such as the Bott index

Relates the Bott index to quantized charge pumping in Thouless pump

Abstract

We propose a new kind of geometric effective theory based on curved space-time single valley Dirac theory with spin connection for twisted bilayer graphene under generic twist angle. This model can reproduce the nearly flat bands with particle-hole symmetry around the first magic angle. The band width is near the former results given by Bistritzer-MacDonald model or density matrix renormalization group. Even more, such geometric formalism allows one to predict the properties of rotating bilayer graphene which cannot be accessed by former theories. As an example, we investigate the Bott index of a rotating bilayer graphene. We relate this to the two-dimensional Thouless pump with quantized charge pumping during one driving period which could be verified by transport measurement.