Parallel Transport of Electrons in Graphene Parallels Gravity

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

Scientific paper

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4 pages

Scientific paper

10.1103/PhysRevB.82.073405

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.

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