Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ<Superscript>-1</Superscript>. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv<Subscript>0</Subscript>≪ T≪ω is equal to σ(ω,k)=e<Superscript>2</Superscript>/4ħ and independent of the band structure parameters γ and v<Subscript>0</Subscript>. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007