Quantum critical transport in clean graphene

Abstract

We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than k_B T/hbar (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. 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) quasi-particles and -holes 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 non-equilibrium distribution functions and the quantum critical conductivity exactly to leading order in 1/|ln(alpha)| where alpha is the coupling constant characterizing the Coulomb interactions.Comment: 19 pages, 1 figure; (v2) added comment on hydrodynamic long-time tail

Hydrodynamics in graphene: Linear-response transport

“…Recently, the kinetic equation approach was applied to electronic excitations in graphene [4][5][6][7][8][9][10][11]. In contrast to conventional metals and semiconductors, graphene is characterized by a linear excitation spectrum, which makes the system explicitly non-Galilean-invariant [6][7][8]12,13].…”

“…In contrast to conventional metals and semiconductors, graphene is characterized by a linear excitation spectrum, which makes the system explicitly non-Galilean-invariant [6][7][8]12,13]. Consequently, the transport scattering time in graphene is strongly affected by the electron-electron interaction [14], which has to be taken into account on equal footing with disorder.…”

“…Consequently, the transport scattering time in graphene is strongly affected by the electron-electron interaction [14], which has to be taken into account on equal footing with disorder. At the same time, due to the classical nature of the Coulomb interaction between charge carriers in graphene, the system is also non-Lorentz-invariant [6][7][8]12,13]. As a result, the standard derivation [1,10,12,13] of the hydrodynamic equations has to be revisited [5][6][7].…”

“…This kinematic peculiarity results in a singular contribution to the collision integral [4,6,8,11,14,15] allowing for a nonperturbative solution to the kinetic equation. A distinct feature of this solution is fast unidirectional thermalization [11] that facilitates integration of the kinetic equation.…”

“…[4,6,8,11] in order to integrate the quantum kinetic equation, we argue that the physics of the system should be described in terms of three macroscopic currents [21,22]: the electric current j , energy current Q, and quasiparticle imbalance [9] current P. In some sense, our approach unifies the above two types of two-fluid description of graphene, where the two macroscopic currents considered are either j and Q (see Refs. [4,6,8,11]), or j and P (see Refs. [9,10]).…”