Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations
By Charles Fefferman, Michael I. Weinstein. 2012
144 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/43e293e3cfefeabe4000e76b232b8399d89b6c84
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
Citations in the corpus
- An overview of periodic elliptic operators (2015, background): “An example popular nowadays is of graphene, where the Dirac cones lead to conductance as if governed by the massless Dirac equation [135,136,218].”