Berry phase in graphene: a semiclassical perspective

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

References in corpus (3)

• Electric Field Effect in Atomically Thin Carbon Films
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy

Cited by in corpus (9)

• Conformal mapping and shot noise in graphene
• Bound states in inhomogeneous magnetic field in graphene: a semiclassical approach
• How to detect the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum
• Graphene n-p junction in a strong magnetic field: a semiclassical study
• Landau levels and magnetic oscillations in gapped Dirac materials with intrinsic Rashba interaction
• Effects of a tilted magnetic field in a Dirac double layer
• Graphene Andreev Billiards
• Quantum corrections to transport in graphene: a trajectory-based semiclassical analysis
• Photoluminescence quenching in gold - MoS2 hybrid nanoflakes