Parallel transport of electrons in graphene parallels gravity

Abstract

Geometrically a crystal containing dislocations and disclinations can be envisaged as a "fixed frame" Cartan-Einstein space-time carrying torsion and curvature, respectively. We demonstrate that electrons in defected graphene are transported in the same way as fundamental Dirac fermions in a nontrivial 2+1 -dimensional space-time, with the proviso that the graphene electrons remember the lattice constant through the valley quantum numbers. The extra "valley holonomy" corresponds to modified Euclidean symmetry generators. © 2010 The American Physical Society.