Parallel Transport of Electrons in Graphene Parallels Gravity


Abstract in English

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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