We study the thermal and electric transport of a fluid of interacting Dirac fermions using a Boltzmann approach. We include Coulomb interactions, a dilute density of charged impurities, and the presence of a magnetic field to describe both the static and the low-frequency response as a function of temperature $T$ and chemical potential $\mu$. In the quantum-critical regime $\mu \lesssim T$ we find pronounced deviations from Fermi-liquid behavior, such as a collective cyclotron resonance with an intrinsic collision-broadened width and significant enhancements of the Mott and Wiedemann-Franz ratios. Some of these results have been anticipated by a relativistic hydrodynamic theory, whose precise range of validity and failure at large fields and frequencies we determine. The Boltzmann approach allows us to go beyond the hydrodynamic regime and to quantitatively describe the deviations from magnetohydrodynamics and the crossover to disorder-dominated Fermi-liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields. Finally, we obtain the full frequency and doping dependence of the single universal conductivity ${\sigma }_Q$ which parametrizes the hydrodynamic response.

• Received 9 June 2008

DOI:https://doi.org/10.1103/PhysRevB.78.115406