Communications in Mathematical Physics

, Volume 326, Issue 1, pp 251–286 | Cite as

Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations

  • Charles L. Fefferman
  • Michael I. WeinsteinEmail author


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 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.


Brillouin Zone Dirac Equation Weinstein Conical Singularity Conical Point 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA

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