Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene

TL;DR

This paper presents a theoretical framework for analyzing Landau levels and magneto-optics in 30° twisted bilayer graphene, revealing unique spectral features and symmetry-driven optical transition rules.

Contribution

It introduces a quasi-band formalism to understand Landau levels in quasicrystalline systems, linking them to quasi-band structures and symmetry-based quantum numbers.

Findings

Identified nearly flat bands with weak magnetic-field dependence.

Discovered highly degenerate levels from twelve off-center pockets.

Predicted optical transition rules based on 12-fold symmetry.

Abstract

We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical interpretation by directly relating the Landau levels to the quasi-band structure, allowing them to be understood as quantized orbits of quasi-band pockets. By using this method, we reveal distinctive spectral features, including nearly flat bands with weak magnetic-field dependence and highly degenerate levels arising from twelve off-center pockets. The resulting Landau levels are classified by two quantum numbers: the Landau-level index and the angular momentum associated with the underlying quasicrystalline symmetry. We also compute the magneto-optical conductivity and show that optical transitions follow angular-momentum selection rules enforced by the 12-fold symmetry. Our approach provides a symmetry-based and computationally efficient framework for bulk quantum magneto-optics in quasicrystalline van der Waals systems, predicting spectroscopic signatures accessible in high-field infrared and THz experiments.