Landau problem for bilayer graphene: Exact results

TL;DR

This paper derives the exact Landau level spectrum for bilayer graphene in a tilted magnetic field, revealing a new SU(2) symmetry at high in-plane field strength, advancing understanding of quantum states in graphene systems.

Contribution

It provides an exact analytical solution for the Landau levels in bilayer graphene under arbitrary magnetic field orientation, uncovering a novel SU(2) symmetry in the high in-plane field limit.

Findings

Exact Landau level spectrum derived for tilted magnetic fields.

Identification of a two-fold degeneracy at large in-plane fields.

Discovery of a new SU(2) symmetry in the system.

Abstract

We consider graphene bilayer in a constant magnetic field of arbitrary orientation (i.e. tilted with respect to the graphene plane). In the low energy approximation to tight binding model with Peierls substitution, we find the exact spectrum of Landau levels. This spectrum is two-fold degenerate in the limit of large in-plane field, which gives rise to a new SU(2) symmetry in this limit.