# Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking

## TL;DR

This paper investigates how symmetry breaking, particularly $C_3$ and $C_2$ symmetries, influences Landau level degeneracy in twisted bilayer graphene near the magic angle, supported by numerical analysis.

## Contribution

It proposes $C_3$ symmetry breaking as the key mechanism for degeneracy lifting in Landau levels, supported by numerical results, and explores the impact of $C_2$ symmetry breaking.

## Key findings

- Degeneracy reduces from eight-fold to four-fold near the magic angle.
- $C_3$ symmetry breaking explains robust degeneracy lifting.
- $C_2$ symmetry breaking also affects Landau level structure.

## Abstract

The degeneracy of Landau levels flanking charge neutrality in twisted bilayer graphene is known to change from eight-fold to four-fold when the twist angle is reduced to values near the magic angle of $\approx 1.05^\circ$. This degeneracy lifting has been reproduced in experiments by multiple groups, and is known to occur even in devices which do not harbor the correlated insulators and superconductors. We propose $C_3$ symmetry breaking as an explanation of such robust degeneracy lifting, and support our proposal by numerical results on the Landau level spectrum in near-magic-angle twisted bilayer graphene. Motivated by recent experiments, we further consider the effect of $C_2$ symmetry breaking on the Landau levels.