Honeycomb Lattice Potentials and Dirac Points

By Charles Fefferman, Michael I. Weinstein. 2012

244 citations recorded by the source corpus.

We prove that the two-dimensional Schroedinger operator with a potential having the symmetry of a honeycomb structure has dispersion surfaces with conical singularities (Dirac points) at the vertices of its Brillouin zone. No assumptions are made on the size of the potential. We then prove the robustness of such conical singularities to a restrictive class of perturbations, which break the honeycomb lattice symmetry. General small perturbations of potentials with Dirac points do not have Dirac points; their dispersion surfaces are smooth. The presence of Dirac points in honeycomb structures is associated with many novel electronic and optical properties of materials such as graphene.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fc35f69a2d05446755bbd7ecb373c99c9323643

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

In Mathematical Physics

Citations in the corpus

Wave Packets in Honeycomb Structures and Two-Dimensional Dirac Equations (2012, background): “These results extend those of [10] and, in particular, include the case of a uniformly strained honeycomb structure.”
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].”
Topological photonics (2018, background): “continuous topological systems can be found in a series of works by Fefferman and Weinstein (2012); Fefferman et al. (2014); Fefferman and Weinstein (2014); and LeeThorp et al.”