Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
Abstract
Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be σ=σ0(1+0.01 g), where 'g' is the dimensionless ("fine structure") coupling constant. The calculations are performed using three different methods: i) electron polarization function, ii) Kubo formula for the conductivity, iii) quantum transport equation. Surprisingly, these methods yield different results unless a proper ultraviolet cut-off procedure is implemented, which requires that the interaction potential in the effective Dirac Hamiltonian is cut-off at small distances (large momenta).
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