# Universal Features of Landau Fans of Twisted Bilayer Graphene with Large Superlattices

## TL;DR

This paper identifies universal features in the Landau fan behavior of twisted bilayer graphene with large superlattices, suggesting a common underlying pattern influenced by Hubbard-like physics and symmetry breaking.

## Contribution

It introduces a Hubbard-like model with mean fields to explain the universal Landau fan features across different TBG samples, highlighting the interplay of Mott physics and symmetry breaking.

## Key findings

- Universal Landau fan dispersion patterns identified
- Degeneracy reduction linked to insulating phases
- Model explains sample-dependent behaviors

## Abstract

Current experiments on different samples of twisted bilayer graphene (TBG) have found different sets of insulating phases. Despite this diversity, many features of these insulating phases appear to be universal. They include the dispersion of Landau fans away from charge neutrality, a reduced Landau fan degeneracy from the expected value at charge neutrality, and the further reduction of this degeneracy when crossing an insulating phase with odd number of electrons in the superlattice unit cell. We point out that all these behaviors as well as the ferromagnetic behavior observed in some of the insulating states suggest an underlying "ideal" pattern, with different part of it realized in the different samples in different experiments. We further show that such pattern can be accounted for by a Hubbard like model for the superlattice augmented with a set of chemical potential dependent mean fields that break the symmetry of the eight internal degrees of freedoms successively. The simultaneous importance of Mott like physics and mean field physics may be a general feature of twisted 2D electronic materials with large superlattices, not necessarily confined to graphene.