Dynamical conductivity of ungated suspended graphene

TL;DR

This paper investigates the frequency-dependent conductivity of suspended graphene with Coulomb interactions and disorder, revealing that at neutrality point the a.c. conductivity varies with frequency depending on disorder and interaction parameters.

Contribution

It provides a low-energy theoretical description of disordered, interacting graphene and characterizes the frequency-dependent conductivity near the neutrality point.

Findings

a.c. conductivity is not frequency independent at neutrality

Conductivity can increase or decrease with decreasing frequency depending on disorder and Coulomb coupling

Results are asymptotically exact for small disorder variances and Coulomb interaction

Abstract

Frequency dependent conductivity of Coulomb interacting massless Dirac fermions coupled to random scalar and random vector potentials is found as a function of frequency in the regime controlled by a line of fixed points. Such model provides a low energy description of a weakly rippled suspended graphene. The main finding is that at the neutrality point the a.c. conductivity is not frequency independent and may either increase or decrease with decreasing frequency, depending on the values of the disorder variances $\Delta_{\phi}$, $\Delta_{A}$ and the Coulomb coupling $\alpha=e^2/(\eps v_F)$. The low frequency behavior is characterized by the values of two dimensionless parameters $\gamma=\Delta_{\phi}/\alpha^2$ and $\Delta_A$ which are RG invariants, and for small values of which the electron-hole "puddles" are effectively screened making the results asymptotically exact.