Geodesic
Honeycomb lattice potentials and Dirac points
Fefferman, Charles1 ; Weinstein, Michael2
1 Department of Mathematics, Princeton University, Fine Hall, Princeton, New Jersey 08544
2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027
Journal of the American Mathematical Society, Tome 25 (2012) no. 4, pp. 1169-1220

Voir la notice de l'article provenant de la source American Mathematical Society

We prove that the two-dimensional Schrödinger 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.
DOI : 10.1090/S0894-0347-2012-00745-0

Fefferman, Charles 1 ; Weinstein, Michael 2

1 Department of Mathematics, Princeton University, Fine Hall, Princeton, New Jersey 08544
2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 
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Fefferman, Charles; Weinstein, Michael. Honeycomb lattice potentials and Dirac points. Journal of the American Mathematical Society, Tome 25 (2012) no. 4, pp. 1169-1220. doi: 10.1090/S0894-0347-2012-00745-0

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