Wave packets in Honeycomb Structures and Two-Dimensional Dirac Equations

Abstract

In a recent article [10], the authors proved that the non-relativistic Schrödinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta, which are located at the vertices of the Brillouin zone, a regular hexagon. In this paper, we study the time-evolution of wave-packets, which are spectrally concentrated near such conical points. We prove that the large, but finite, time dynamics is governed by the two-dimensional Dirac equations.

34 pages, 2 figures

References in corpus (2)

• The electronic properties of graphene
• Photonic Floquet Topological Insulators

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