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arXiv · 0909.2703

Parallel Transport of Electrons in Graphene Parallels Gravity

Andrej Mesaros·Darius Sadri·Jan Zaanen
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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.

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Andrej Mesaros, Darius Sadri, Jan Zaanen. 2009-09-15. Parallel Transport of Electrons in Graphene Parallels Gravity. https://doi.org/10.1103/physrevb.82.073405

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