Coulomb drag in graphene: perturbation theory

B. N. Narozhny; M. Titov; I. V. Gornyi; P. M. Ostrovsky

doi:10.1103/PhysRevB.85.195421

paper

Coulomb drag in graphene: perturbation theory

arXiv:1110.6359 · doi:10.1103/PhysRevB.85.195421

Abstract

We study the effect of Coulomb drag between two closely positioned graphene monolayers. In the limit of weak electron-electron interaction and small inter-layer spacing ( $μ_{1 (2)}, T ≪ v / d$ ) the drag is described by a universal function of the chemical potentials of the layers $μ_{1 (2)}$ measured in the units of temperature $T$ . When both layers are tuned close to the Dirac point, then the drag coefficient is proportional to the product of the chemical potentials $ρ_{D} \propto μ_{1} μ_{2}$ . In the opposite limit of low temperature the drag is inversely proportional to both chemical potentials $ρ_{D} \propto T^{2} / (μ_{1} μ_{2})$ . In the mixed case where the chemical potentials of the two layers belong to the opposite limits $μ_{1} ≪ T ≪ μ_{2}$ we find $ρ_{D} \propto μ_{1} / μ_{2}$ . For stronger interaction and larger values of $d$ the drag coefficient acquires logarithmic corrections and can no longer be described by a power law. Further logarithmic corrections are due to the energy dependence of the impurity scattering time in graphene (for $μ_{1 (2)} ≫ T$ these are small and may be neglected). In the case of strongly doped (or gated) graphene $μ_{1 (2)} ≫ v / d ≫ T$ the drag coefficient acquires additional dependence on the inter-layer spacing and we recover the usual Fermi-liquid result if the screening length is smaller than $d$ .

22 pages, 8 figure, extended version

Coulomb drag in graphene: perturbation theory

Abstract

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