Investigación

 

Origin of conical dispersion relations

 

Sergio A. Hojman

 

Departamento de Ciencias, Facultad de Artes Liberales, Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile, and Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile, and Centro de Recursos Educativos Avanzados, CREA, Santiago, Chile. e-mail: sergio.hojman@uai.cl

 

Received 28 January 2014;
Accepted 23 June 2014

 

Abstract

A mechanism that produces conical dispersion relations is presented. A Kronig Penney one dimensional array with two different strengths delta function potentials gives rise to both the gap closure and the dispersion relation observed in graphene and other materials. The Schrodinger eigenvalue problem is locally invariant under the infinite dimensional Virasoro algebra near conical dispersion points in reciprocal space, thus suggesting a possible relation to string theory.

Keywords: Quantum mechanics; modified Dirac-Kronig-Penney potential; conical dispersion relations.

 

PACS: 03.65.-w; 03.65.Ge

 

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