Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect

TL;DR

This paper introduces a hybrid Wannier function approach to study strong interactions in twisted bilayer graphene, revealing conditions for the quantized anomalous Hall effect at specific electron fillings.

Contribution

It presents a novel hybrid Wannier function method for analyzing interaction effects in twisted bilayer graphene, focusing on the emergence of the quantized anomalous Hall effect.

Findings

Hybrid Wannier functions effectively describe active bands in twisted bilayer graphene.

Quantized anomalous Hall effect observed at specific electron fillings.

Different regimes identified where the effect is stabilized.

Abstract

We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions, that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moir\'e cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.