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 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.

4 pages

References in corpus (4)

• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Electronic properties of curved graphene sheets
• Geometric Phases in Graphitic Cones
• Dislocations and torsion in graphene and related systems

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