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arXiv 1111.5022cond-mat.mes-hall
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单层和双层石墨烯中的库仑阻力

Coulomb drag in monolayer and bilayer graphene

E. H. Hwang, Rajdeep Sensarma, S. Das Sarma

摘要:

我们从理论上计算了两个石墨烯单层之间以及两个石墨烯双层之间的相互作用引起的摩擦库仑阻力系数,这两个石墨烯双层在空间上分开一个距离"$d$"。我们发现,石墨烯单层之间的阻力可以显着影响层内动量弛豫机制。对于与能量无关的层内散射,由层间电子-电子相互作用引起的摩擦阻力分别在高密度($k_F d \gg 1$)和低密度($k_F d \ll 1$)极限下渐近地变为$ρ_D \sim T^2/n^4d^6$和$ρ_D \sim T^2/n^2d^2$。当长程电荷杂质散射在层内占主导地位时,单层拖曳电阻率分别表现为$k_F d \gg 1$和$k_F d \ll 1$的$ρ_D \sim T^2/n^3d^4$和$T^2 \ln (\sqrt{n} d) /n$。双层阻力的密度依赖性被计算为$ρ_D \propto T^2/n^{3}$在大和小层分离极限。在大的层分离极限,双层阻力有一个强大的$1/d^4$层分离的依赖性,而这到一个弱的对数依赖性的强层间相关性的限制小的层分离。除了获得库仑阻力在石墨烯中的渐近解析公式,我们提供了任意值的密度和层分离的数值结果,我们的渐近理论结果之间的平滑插值。

英文摘要:

We theoretically calculate the interaction-induced frictional Coulomb drag resistivity between two graphene monolayers as well as between two graphene bilayers, which are spatially separated by a distance "$d$". We show that the drag resistivity between graphene monolayers can be significantly affected by the intralayer momentum-relaxation mechanism. For energy independent intralayer scattering, the frictional drag induced by inter-layer electron-electron interaction goes asymptotically as $ρ_D \sim T^2/n^4d^6$ and $ρ_D \sim T^2/n^2d^2$ in the high-density ($k_F d \gg 1$) and low-density ($k_F d \ll 1$) limits, respectively. When long-range charge impurity scattering dominates within the layer, the monolayer drag resistivity behaves as $ρ_D \sim T^2/n^3d^4$ and $T^2 \ln (\sqrt{n} d) /n$ for $k_F d \gg 1$ and $k_F d \ll 1$, respectively. The density dependence of the bilayer drag is calculated to be $ρ_D \propto T^2/n^{3}$ both in the large and small layer separation limit. In the large layer separation limit, the bilayer drag has a strong $1/d^4$ dependence on layer separation, whereas this goes to a weak logarithmic dependence in the strong inter-layer correlation limit of small layer separation. In addition to obtaining the asymptotic analytical formula for Coulomb drag in graphene, we provide numerical results for arbitrary values of density and layer separation interpolating smoothly between our asymptotic theoretical results.

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