Quantum critical transport in clean graphene

TL;DR

The work addresses quantum critical transport in clean graphene at charge neutrality by combining renormalization group analysis with a quantum Boltzmann equation approach. It shows that Coulomb interactions drive a slow flow of the effective coupling $\alpha(T)$ to weak coupling, while preserving a zero scaling dimension for conductivity via gauge invariance. In the collision-dominated regime, the authors derive an exact leading-order result in $1/|\ln(\alpha)|$ for the non-equilibrium distribution and obtain a Drude-like conductivity $\sigma(ω) = (e^2/h) N k_B T \ln 2 / [-i \hbar ω + κ k_B T α^2]$ with $κ ≈ 3.646$ for $N=4$, revealing the central role of logarithmically enhanced collinear scattering. The findings illuminate how quantum critical physics and hydrodynamic behavior emerge in graphene and specify conditions under which these effects could be experimentally observed, including the importance of long inelastic lengths and preserved particle-hole symmetry.

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.

Figures (1)

• Figure 1: Illustration of the Golden rule diagrams entering the collision term. The diagrams (a) describe scattering of oppositely charged particles corresponding to the term $R_1$, while the diagrams (b) describe scattering of like particles corresponding to the term $R_2$. Note that the vertex preserves the flavor $a=i,j$, but not the particle/hole nature $\lambda=\pm$. The factor $1/2$ of the first diagram accounts for the symmetry factor associated with having two indistinguishable particles in the final state.