Charles L. Fefferman, Michael I. Weinstein
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.
View original:
http://arxiv.org/abs/1202.3839
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