Theory of Coulomb drag for massless Dirac fermions

Abstract

Coulomb drag between two unhybridized graphene sheets separated by a dielectric spacer has recently attracted considerable theoretical interest. We first review, for the sake of completeness, the main analytical results which have been obtained by other authors. We then illustrate pedagogically the minimal theory of Coulomb drag between two spatially separated two-dimensional systems of massless Dirac fermions which are both away from the chargeneutrality point. This relies on second-order perturbation theory in the screened interlayer interaction and on Boltzmann-transport theory. In this theoretical framework and in the low-temperature limit, we demonstrate that, to leading (i.e. quadratic) order in temperature, the drag transresistivity is completely insensitive to the precise intralayer momentum-relaxation mechanism (i.e. to the functional dependence of the transport scattering time on energy). We also provide analytical results for the low-temperature drag transresistivity for both cases of 'thick' and 'thin' spacers and for arbitrary values of the dielectric constants of the media surrounding the two Dirac-fermion layers. Finally, we present numerical results for the low-temperature drag transresistivity for the case when one of the media surrounding the Dirac-fermion layers has a frequencydependent dielectric constant. We conclude by suggesting an experiment that can potentially allow for the observation of departures from the canonical quadraticin-temperature behavior of the transresistivity.

Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures

“…47 to include effects due to the finite width of the GaAs quantum well (see Supplementary Note 4). This shows that the experimental results in this temperature range are consistent with the canonical Fermi-liquid prediction 24,[43][44][45][46][47][48][49][50] , that is, R D pT 2 (see also Fig. 3a), as constrained by the available phase-space of the initial and final states involved in the scattering process.…”

“…Figure 2d shows the plots of R D for 30 KrTr50 K, with the 2DEG used as the drive (black points) or passive (red points) layer. It also reports calculations of the temperature dependence of R D in a hybrid Dirac/Schrödinger SLG/2DEG double layer within a Boltzmanntransport theory, which is justified in the Fermi-liquid regime 47,48 . This is done by generalizing the theory of ref.…”

Coulomb drag

“…The strongly doped, Fermi-liquid regime has attracted the most attention in literature. Most authors report the standard ρ D ∼ T 2 n −3 d −4 behavior (Amorim and Peres, 2012;Carrega et al, 2012;Hwang et al, 2011;Katsnelson, 2011;Narozhny et al, 2012; assuming the energy-independent impurity scattering time.…”

“…Both papers reported a stronger dependence of the drag coefficient on the carrier density and interlayer separation, ρ D ∼ T 2 n −4 d −6 . This result was later disputed in ; Carrega et al (2012);and Narozhny et al (2012). These authors showed that the energy (or momentum) dependence of τ is qualitatively irrelevant for the asymptotic behavior of ρ D .…”

“…21 and 22 below, includes the contribution was automatically by using the dynamically screened interaction propagator (7). At the same time, quantitative description of experiments, especially in devices with wider interlayer spacing, might be significantly affected by such aspects as inhomogeneous dielectric background (Badalyan and Peeters, 2012;Carrega et al, 2012) and hybridization between phonon and plasmon modes . Plasmon-mediated drag between graphene wave-guides was suggested in Shylau and Jauho (2014).…”