Discrete symmetry in graphene: the Dirac equation and beyond

TL;DR

This paper reviews discrete symmetries of the Dirac equation in different dimensions and explores their implications in graphene, including effects of lattice deformations and symmetry breaking.

Contribution

It provides a comparative pedagogical analysis of Dirac symmetries in 3+1 and 2+1 dimensions and extends to full lattice models in graphene.

Findings

Discrete symmetries differ between 3+1 and 2+1 dimensions.

Full lattice models reveal symmetry breaking effects.

Deformations and second-neighbor interactions affect CPT symmetry.

Abstract

In this pedagogical 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, 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.