Enhancement of Coulomb drag in double-layer graphene structures by plasmons and dielectric background inhomogeneity

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Enhancement of Coulomb drag in double-layer graphene structures by plasmons and dielectric background inhomogeneity

S. M. Badalyan and F. M. Peeters

Phys. Rev. B 86, 121405(R) – Published 20 September 2012

Abstract

The drag of massless fermions in graphene double-layer structures is investigated over a wide range of temperatures and interlayer separations. We show that the inhomogeneity of the dielectric background in such graphene structures, for experimentally relevant parameters, results in a significant enhancement of the drag resistivity. At intermediate temperatures the dynamical screening via plasmon-mediated drag enhances the drag resistivity and results in an upturn in its behavior at large interlayer separations. In a range of interlayer separations, corresponding to the crossover from strong to weak coupling of graphene layers, we find that the decrease of the drag resistivity with interlayer spacing is approximately quadratic. This dependence weakens below this range of interlayer spacing while for larger separations we find a cubic (quartic) dependence at intermediate (low) temperatures.

Received 20 April 2012

DOI:https://doi.org/10.1103/PhysRevB.86.121405

Authors & Affiliations

S. M. Badalyan^* and F. M. Peeters

Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

^*Samvel. Badalyan@ua.ac.be

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Issue

Vol. 86, Iss. 12 — 15 September 2012

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Images

Figure 1
Left: A graphene double-layer system immersed in a three-layer dielectric medium. The solid lines with spacing $d$ represent the active and passive graphene layers, 1 and 2, separating different materials with dielectric permittivities $ε_{1}$ , $ε_{2}$ , and $ε_{3}$ . Right: The solid curve corresponds to the ratio of the double-layer screening functions $ɛ_{s}^{h} (q)$ to $ɛ_{s} (q)$ , which are calculated within the static screening approximation, respectively, in GDLSs with a homogeneous average dielectric permittivity ${\bar{ε}}_{13}$ and in GDLSs with a nonhomogeneous dielectric background, corresponding to the three-layered medium of the left figure. The dotted, dashed, and dotted-dashed curves show, respectively, the intra- and interlayer effective dielectric functions ${\bar{ε}}_{11} (q d)$ , ${\bar{ε}}_{22} (q d)$ , and ${\bar{ε}}_{12} (q d)$ in units of ${\bar{ε}}_{13}$ . The electron density in each graphene layer is $n_{1} = n_{2} = 10^{12}$ cm $^{- 2}$ and $d = 5$ nm that corresponds to $k_{F} d \approx 0.89$ .Reuse & Permissions
Figure 2
The effect of the dielectric background inhomogeneity on the Coulomb drag in GDLSs. The top pair of symbols shows the log-log plot of the drag resistivity as a function of scaled temperature in GDLSs with $d = 5$ nm interlayer spacing, immersed in a nonhomogeneous (the upper set) and homogeneous (the lower set) dielectric background with the parameters of the GDLS of Fig. 1. The two other pairs of data sets in the middle and bottom of the figure correspond, respectively, to $d = 15$ and 30 nm interlayer spacing. All curves have been calculated within the static screening approximation.Reuse & Permissions
Figure 3
Plasmon enhancement of Coulomb drag of massless fermions in GDLSs. The top and bottom bold curves are log-log plots of the drag resistivity vs scaled temperature for $d = 5$ and $d = 30$ nm interlayer spacing, respectively. The solid curves correspond to calculations using the finite temperature exact polarization and nonlinear response functions while the dashed curves are calculated within the static screening approximation. The parameters are the same as in Fig. 1 for GDLSs with a nonhomogeneous dielectric background. The thin curves correspond to the calculations for $d = 5$ nm in GDLSs with a homogeneous dielectric background.Reuse & Permissions
Figure 4
The log-log plot of the drag resistivity as a function of the interlayer spacing $d$ for $T = 0.2 T_{F}$ (the solid and dashed curves) and for $T = 0.1 T_{F}$ (the dotted-dashed and dotted curves). The solid curve corresponds to calculations using the finite temperature exact polarization and nonlinear response functions, and the other curves are based on the static screening approximation. The dotted curve is calculated for GDLSs with a homogeneous dielectric background, and the other curves for GDLSs with a nonhomogeneous dielectric background. The parameters are the same as in Fig. 1.Reuse & Permissions

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