Berry phase in graphene: a semiclassical perspective

TL;DR

This paper develops a semiclassical framework for understanding the Berry phase in graphene, highlighting its relation to the adiabatic Berry phase and applying it to derive Landau levels in different configurations.

Contribution

It introduces a semiclassical expression for the Green's function in graphene that explicitly includes a phase related to the Berry phase, with applications to Landau level derivations.

Findings

Semiclassical phase coincides with Berry phase for linear Dirac dispersion.

Differences between phases emerge when a gap is introduced at the Dirac point.

Semiclassical formalism successfully derives Landau levels in various graphene configurations.

Abstract

We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, illustrating the role of the semiclassical ``Berry-like'' phase