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+0.01 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).Comment: 5 pages, 1 figure; Reply to the Comment by I.F. Herbut, V. Juricic, O. Vafek, and M.J. Case, "Comment on "Minimal conductivity in graphene: Interaction corrections and ultraviolet anomaly" by Mishchenko E. G.", arXiv:0809.0725, is added in Appendi

Effect of electron-electron interactions on the conductivity of clean graphene

Minimal conductivity of a single undoped graphene layer is known to be of the order of the conductance quantum, independent of the electron velocity. We show that this universality does not survive electron-electron interaction which results in the non-trivial frequency dependence. We begin with analyzing the perturbation theory in the interaction parameter 'g' for the electron self-energy and observe the failure of the random-phase approximation. The optical conductivity is then derived from the quantum kinetic equation and the exact result is obtained in the limit when g << 1 << g ln\omega.Comment: 4 pages, 3 figures; final versio

Transport equations for a two-dimensional electron gas with spin-orbit interaction

The transport equations for a two-dimensional electron gas with spin-orbit interaction are presented. The distribution function is a 2x2-matrix in the spin space. Particle and energy conservation laws determine the expressions for the electric current and the energy flow. The derived transport equations are applied to the spin-splitting of a wave packed and to the calculation of the structure factor and the dynamic conductivity.Comment: 6 pages, 1 figure, revised versio