Investigación

 

Discrete symmetry in graphene: the Dirac equation and beyond

 

E. Sadurní, E. Rivera-Mociños, and A. Rosado

 

Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, México. e-mail: sadurni@ifuap.buap.mx;erivera@ifuap.buap.mx;rosado@ifuap.buap.mx

 

Received 5 January 2015;
accepted 9 February 2015

 

Abstract

In this paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d Dirac equation in condensed matter (e.g. graphene), we further analyze the discrete symmetries of a full tight-binding model in hexagonal lattices without conical approximations. We touch upon an effective CPT symmetry breaking that occurs when deformations and second-neighbor corrections are considered.

Keywords: 2d Dirac equation; discrete symmetries; graphene; boron nitride.

 

Resumen

En este artículo revisamos las simetrías discretas de la ecuación de Dirac usando herramientas fundamentales, en un orden comparativo: el caso commi 3 + 1 dimensional y el caso reducido 2 + 1 dimensional. Motivados por nuevas aplicaciones de la ecuación de Dirac 2d en materia condensada (v. gr. grafeno), también analizamos las simetrías discretas de un modelo de amarre fuerte en redes hexagonales más allá de las aproximaciones cónicas. Hacemos breve mención de un rompimiento de simetría CPT efectiva que ocurre cuando se consideran deformaciones de la red e interacciones a segundos vecinos.

Palabras clave: Ecuación de Dirac 2d; simetrías discretas; grafeno; nitruro de boro.

 

PACS: 03.65.Pm; 11.30.Er; 81.05.ue

 

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Acknowledgments

E. S. and E. R.-M. would like to express their gratitude to CONACyT for financial support under project CB2012-180585.

 

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