Wave packets in honeycomb structures and two-dimensional dirac equations

Charles L. Fefferman, Michael I. Weinstein

Research output: Contribution to journalArticle

48 Scopus citations

Abstract

In a recent article (Fefferman and Weinstein, in J Am Math Soc 25:1169– 1220, 2012), 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 wavepackets, 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.

Original languageEnglish (US)
Pages (from-to)251-286
Number of pages36
JournalCommunications In Mathematical Physics
Volume326
Issue number1
DOIs
StatePublished - Nov 29 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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