# Landau levels in twisted bilayer graphene and semiclassical orbits

## TL;DR

This paper provides a detailed theoretical analysis of Landau levels in twisted bilayer graphene, highlighting differences in spectra within and outside the magic angle range and connecting these to experimental quantum oscillation observations.

## Contribution

It offers a comprehensive semiclassical and topological analysis of Landau levels in the non-interacting continuum model, elucidating their origin and experimental relevance.

## Key findings

- Distinct butterfly spectra for magic and non-magic angles
- Semiclassical analysis links Landau levels to band structure
- Partial explanation of quantum oscillation features

## Abstract

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1$^\circ$. This is now strongly supported by experiment, which furthermore reveals dramatic correlation effects in the magic range due to the relative dominance of interactions when the bandwidth is suppressed. Experimentally, quantum oscillations exhibit different Landau level degeneracies when the angles fall in or outside the magic range; these observations can contain crucial information about the low energy physics. In this paper, we report a thorough theoretical study of the Landau level structure of the non-interacting continuum model for twisted bilayer graphene as the magnetic field and the twist angle are tuned. We first show that a discernible difference exists in the butterfly spectra when twist angle falls in and outside the magic range. Next, we carry out semiclassical analysis in detail, which quantitatively determines the origin of the low energy Landau levels from the zero field band structure. We find that the Landau level degeneracy predicted in the above analyses is capable of partially explaining features of the quantum oscillation experiments in a natural way. Finally, topological aspects, validity, and other subtle points of the model are discussed.