Honeycomb Lattice Potentials and Dirac Points

Details Honeycomb Lattice Potentials and Dirac Points Honeycomb Lattice Potentials and Dirac Points

2012-02-17

arxiv.org/abs/1202.3839v1

Physics

Mathematical Physics

52 pages, 1 figure

Scientific paper

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 also prove the robustness of such conical singularities to a restricted class of perturbing potentials, 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.

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