General relativity and graphene

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Geometrical description? Gauge theory of linear defecs in solids: metric approach to elasticity M.O. Katanaev <strong>and</strong> I.V. Volovich, Ann. Phys. (N.Y.) 216 (1992) 1 V.A. Osipov, Phys. Lett. A 175 (1993) 65; Physica A 175 ( 1991 ) 369 C. Furtado, F. Moraes, Physics Letters A 188 (1994) 394. H. Kleinert, Gauge fields in condensed matter, vol 2. Dislocations can be described in the covariant formalism by adding torsion to the spacetime connection.
Torsion in differential geometry Basic buildings of geometry in manifolds: Metric tensor Covariant derivative (connection) D v ν ( ν )v ρ = ∂ +Γ { } µ µ µρ Γ = + T ρ ρ ρ µν µν µν The derivative of a vector implies evaluating it at two different points. The vector has to be parallel transported along infinitesimal path dx. In spaces with torsion infinitesimal parallelograms do not close. Autoparallel <strong>and</strong> geodesics are not the same.
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 and 20: Multiple defects
Page 21 and 22: Cosmology versus condensed matter N
Page 23 and 24: Computation of observables Equation
Page 25 and 26: Averaging over disorder A. Cortijo
Page 27: Characterized by the Burgers vector
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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