▎ 摘　　要

We study the effect of Coulomb drag between two closely positioned graphene monolayers, assuming that transport properties of the sample are dominated by disorder. This assumption allows us to develop a perturbation theory in alpha T-2 tau min(1, T/mu(1(2))) << 1 (here, alpha = e(2)/v is the strength of the Coulomb interaction, T is temperature, mu(1(2)) is the chemical potential of the two layers, and tau is the mean-free time). Our theory applies for arbitrary values of mu(1(2)), T, and the interlayer separation d, although we focus on the experimentally relevant situation of low temperatures T < v/d. We find that the drag coefficient rho(D) is a nonmonotonous function of mu(1(2)) and T in qualitative agreement with experiment [S. Kim et al., Phys. Rev. B 83, 161401(R) (2011)]. Precisely at the Dirac point, drag vanishes due to electron-hole symmetry. For very large values of chemical potential mu(1(2)) >> v/(alpha d), we recover the standard Fermi-liquid result rho(FL)(D) alpha T-(n1n2)(2)-3/2d-4 (where ni is the carrier density in the two layers). At intermediate values of the chemical potential, the drag coefficient exhibits a maximum. The decrease of the drag coefficient as a function of mu(1(2)) (or the carrier densities) from its maximum value is characterized by a crossover from a logarithmic behavior rho(D) alpha T-(n1n2)(2)-1/2 ln n(1) to the Fermi-liquid result. Our results do not depend on the microscopic model of impurity scattering. The crossover occurs in a wide range of densities, where rho(D) can not be described by a power law. On the contrary, the increase of the drag from the Dirac point (for mu(1(2)) << v/d) is described by the universal function of mu 1(2) measured in the units of T; if both layers are close to the Dirac point mu(1(2)) << T, then rho(D) alpha mu(1)mu(2)/T-2; in the opposite limit of low temperature, rho(D) alpha T-2/(mu(1)mu(2)) and in the mixed case, mu(1) << T << mu(2), we find rho(D) alpha mu(1)/mu(2).