Quantum Critical Transport in Clean Graphene

Abstract

We describe electrical transport in ideal single-layer graphene at zero applied gate voltage. There is a crossover from collisionless transport at frequencies larger than ${k}_{B}T/\ensuremath{\hbar}$ ($T$ is the temperature) to collision-dominated transport at lower frequencies. The dc conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplitude (a consequence of relativistic dispersion in two dimensions), quasiparticles and quasiholes moving in the same direction tend to an effective equilibrium distribution whose parameters depend on the direction of motion. This property allows us to find the nonequilibrium distribution functions and the quantum critical conductivity exactly to leading order in $1/|\text{ln}(\ensuremath{\alpha})|$, where $\ensuremath{\alpha}$ is the coupling constant characterizing the Coulomb interactions.