General relativity and graphene

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Torsion in General relativity Einstein-Cartan relativity E. Cartan [1] The energy-momentum tensor of a spinor field is antisymmetric and can not be included in [1] Include a general connection with antisymmetric part (torsion). Curvature couples to mass and torsion to spin.
Dirac fermions in curved space with torsion ( ( )) ) v A 5 L = Ψγ µ ∂ −Ω x Ψ + ig Ψγ µ T Ψ+ g Ψγ γ µ S Ψ µ µ µ µ Ω = 1 γ γ e 4 e a b ν µ a; µ bν T = g S , S =ε S ν µ µνρ ρ µ νρ σ µνρσ The trace part of the torsion is associated to edge dislocations –change in volume element - and couples as a usual vector gauge field. The axial part associated to screw dislocations induces an axial coupling that affects the Berry phase of the fermions. In a 2D surface (graphene) only edge dislocations can exist and their (non-minimal) coupling to the electronics degrees of freedom generates –yet another- standard vector gauge field. F. de Juan, A. Cortijo, MAHV, work in progress.
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 and 28: Characterized by the Burgers vector
Page 29: Torsion in differential geometry Ba
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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