Minimal conductivity in graphene: Interaction corrections and ultraviolet anomaly

Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be sigma = sigma(0)(1 + 0.01g), 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). Copyright (C) EPLA, 2008.