Berry phase, semiclassical quantization and Landau levels

TL;DR

This paper develops a semiclassical quantization method incorporating Berry phase effects to analyze Landau levels in complex electron systems, especially where traditional methods are inadequate, such as in bilayer graphene.

Contribution

It introduces an explicit analytical expression for Berry phase in multi-band systems, enabling Landau level evaluation beyond rigorous quantization limits.

Findings

Berry phase expression derived for complex systems

Landau levels estimated in bilayer graphene and graphite

Magnetic breakdown observed in specific electron orbits

Abstract

We propose the semiclassical quantization for complicated electron systems governed by a many-band Hamiltonian. An explicit analytical expression of the corresponding Berry phase is derived. This impact allows us to evaluate the Landau magnetic levels when the rigorous quantization fails, for instance, for bilayer graphene and graphite with the trigonal warping. We find that the magnetic breakdown can be observed for the certain type of classical electron orbits.