Parallel Transport of Electrons in Graphene Parallels Gravity

TL;DR

This paper shows that electrons in defected graphene experience transport analogous to Dirac fermions in curved space-time, with their valley quantum numbers encoding the lattice's geometric effects, linking condensed matter physics with gravitational concepts.

Contribution

It introduces a geometric framework for understanding electron transport in defected graphene using concepts from gravity and space-time torsion and curvature.

Findings

Electrons in graphene behave as Dirac fermions in a curved space-time.

Valley quantum numbers encode lattice geometry effects.

Modified Euclidean symmetry generators relate to valley holonomy.

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 non-trivial 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.