Kinetic theory of Coulomb drag in two monolayers of graphene: From the Dirac point to the Fermi liquid regime

We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Using a Boltzmann equation approach, we study a variety of limits ranging from the nondegenerate interaction-dominated limit close to charge neutrality all the way to the Fermi liquid regime. In the nondegenerate limit, we find that the presence of the passive layer can largely influence the conductivity of the active layer despite the absence of drag. This induces a nontrivial temperature behavior of the single-layer conductivity and furthermore suggests a promising strategy towards increasing the role of inelastic scattering in future experiments. For small but finite chemical potential, we find that the drag resistivity varies substantially as a function of the ratio of inelastic and elastic scattering. Furthermore, we explicitly show that the clean system has a well-defined drag resistivity even though the individual conductivities diverge. We find that an extrapolation from finite chemical potential to zero chemical potential and to the clean system is delicate and the order of limits matters. The limiting value is either zero or equal to the inverse of the interaction-dominated single-layer conductivity sigma(0) of clean graphene and in that sense is a universal number. In the Fermi liquid regime, we analyze drag as a function of temperature T and the distance d between the layers and compare our results to existing theoretical and experimental results. In addition to the conventional 1/d(4) dependence with an associated T-2 behavior, we find there is another regime of 1/d(5) dependence where drag varies in linear-in-T fashion. The relevant parameter separating these two regimes is given by (d) over bar = Td/nu(F) (nu(F) is the Fermi velocity), where (d) over bar << 1 corresponds to T-2 behavior, while (d) over bar >> 1 corresponds to T behavior. We speculate that the broad crossover between these two regimes was observed in recent experiments on graphene as well as in old experiments on conventional two-dimensional electron gases. We close with a discussion of the role of screening and the determination of the drag resistivity as a function of the charge-carrier densities in the two layers under very general circumstances covering the whole crossover from the nondegenerate to the degenerate limit in both layers independently.