General relativity and graphene

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Generalization A. Cortijo and MAHV, EPL (07), Nucl. Phys. B (07). Cosmic strings induce conical defects in the universe. The motion of a spinor field in the resulting curved space is known in general relativity. Generalize the geometry of a single string by including negative deficit angles (heptagons). Does not make sense in cosmology but it allows to model graphene with an arbitrary number of heptagons and pentagons. 2 2 −2 Λ( xy , ) 2 2 ds =− dt + e ( dx + dy ) N ∑ Λ ( r) = 4µ log( r) , r = ⎡ ⎣( x− a ) + ( y−b) i= 1 2 2 i i i i i The metric of N cosmic strings located at (a, b) i with deficit (excess) angles µ i . ⎤ ⎦ 1/2
Cosmology versus condensed matter NASA's Spitzer Space Telescope. • G. E. Volovik: “The universe in a helium droplet”, Clarendon press, Oxford 2000. • Bäuerle, C., et al. Laboratory simulation of cosmic string formation in the early universe using superfluid 3 He. Nature 382:332-334 (1996). • Bowick, M., et al. The cosmological Kibble mechanism in the laboratory: String formation in liquid crystals. Science 236:943-945 (1994). We play the inverse game: use cosmology to model graphene
Page 1 and 2: Evora08 General relativity and grap
Page 3 and 4: A brief history of graphene In the
Page 5 and 6: Second revolution: graphene (05) Wh
Page 7 and 8: Other interesting points of the dis
Page 9 and 10: Ripples on graphene Freely suspende
Page 11 and 12: Physical origin of the curvature
Page 13 and 14: Observation of topological defects
Page 15 and 16: Formation of topological defects Sq
Page 17 and 18: Dirac in curved space We can includ
Page 19: Multiple defects
Page 23 and 24: Computation of observables Equation
Page 25 and 26: Averaging over disorder A. Cortijo
Page 27 and 28: Characterized by the Burgers vector
Page 29 and 30: Torsion in differential geometry Ba
Page 31 and 32: Dirac fermions in curved space with
Page 33 and 34: arXiv:0810.5121 Similar models. Fut
Page 35 and 36: Summary • Ripples occur naturally
Page 37: Conclusions General relativity and

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