Journal
ANNALS OF PHYSICS
Volume 327, Issue 11, Pages 2617-2626Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2012.05.013
Keywords
Graphene; Black hole; BTZ black hole; Optical geometry
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Funding
- DoE [DOE-EY-76-02-3071]
- NSF RTG DMS [0636606]
- Fay R. and Eugene L. Langberg Endowed Chair
- Slovenian Research Agency (ARRS)
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0636606] Funding Source: National Science Foundation
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It is well known that the low energy electron excitations of the curved graphene sheet Sigma are solutions of the massless Dirac equation on a 2 + 1 dimensional ultra-static metric on R x Sigma. An externally applied electric field on the graphene sheet induces a gauge potential which could be mimicked by considering a stationary optical metric of the Zermelo form, which is conformal to the BTZ black hole when the sheet has a constant negative curvature. The Randers form of the metric can model a magnetic field, which is related by a boost to an electric one in the Zermelo frame. We also show that there is a fundamental geometric obstacle to obtaining a model that extends all the way to the black hole horizon. (C) 2012 Elsevier Inc. All rights reserved.
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