Space-time dispersion of graphene conductivity

TL;DR

This paper provides an analytical study of graphene's conductivity dependence on frequency, wave-vector, and temperature, offering simple formulas in various limits and explaining experimental observations in graphite.

Contribution

It presents the first comprehensive analytical expressions for graphene's conductivity across different regimes, incorporating effects of frequency, wave-vector, and temperature.

Findings

Conductivity at $kv_{0} r T r \omega$ equals $e^{2}/4 r \hbar$ and is independent of band parameters.

Derived asymptotic expressions for conductivity in various limiting cases.

Explained the temperature and pressure dependence of graphite conductivity.

Abstract

We present an analytic calculation of the conductivity of pure graphene as a function of frequency $\omega $, wave-vector $k$, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter $\gamma =3$ eV. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for $kv_{0}\ll T\ll \omega $ is equal to $\sigma (\omega, k)=e^{2}/4\hbar $ and independent of the band structure parameters $\gamma $ and $v_{0}$. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.