Coulomb Drag in Graphene Near the Dirac Point

We study Coulomb drag in graphene near the Dirac point, focusing on the regime of interaction-dominated transport. We establish a novel, graphene-specific mechanism of Coulomb drag based on fast interlayer thermalization, inaccessible by standard perturbative approaches. Using the quantum kinetic equation framework, we derive a hydrodynamic description of transport in double-layer graphene in terms of electric and energy currents. In the clean limit the drag becomes temperature independent. In the presence of disorder the drag coefficient at the Dirac point remains nonzero due to higher-order scattering processes and interlayer disorder correlations. At low temperatures (diffusive regime) these contributions manifest themselves in the peak in the drag coefficient centered at the neutrality point with a magnitude that grows with lowering temperature.

Figure 1

Leading-order drag coefficient in the ballistic regime as a function of carrier densities (in units of ${10}^{11}{\mathrm{cm}}^{-2}$) for $d=9\mathrm{nm}$. Left: ${\rho }_D$ at $T=250\mathrm{K}$; the upper left panel refers to ultraclean graphene ${\tau }^{-1}=0.5\mathrm{K}$; the lower left panel shows the evolution of ${\rho }_D$ with increasing disorder from ${\tau }^{-1}=0$ to ${\tau }^{-1}=50\mathrm{K}$. Right: ${\rho }_D$ for ${\tau }^{-1}=50\mathrm{K}$; the lower panel shows ${\rho }_D$ for $T=150$, 200, 250, and 300 K.

Figure 2

Drag coefficient for identical layers, $\mu \ll \min (T/\alpha ,v/d)$, and uncorrelated disorder. Bottom row (${\tau }^{-1}\ll {\alpha }^{2}T$ and below the curve 2, ${\tau }^{-1}\ll {\alpha }^2{T}^2/\mu$): solutions of the QKE (12). Curve 1 (${\tau }^{-1}={\alpha }^2{\mu }^2/T$) separates the two regimes in Eq. (14). Middle row (${\alpha }^{2}T\ll {\tau }^{-1}\ll T$): region where the QKE approach overlaps with the perturbation theory of Ref. 16. The third-order contribution ${\rho }_D^{(3)}=\mathcal{O}({\alpha }^3)$ yielding nonzero drag at $\mu =0$ is shown in red. Upper row (${\tau }^{-1}\gg T$): diffusive regime [see Eqs. (16, 17)], where ${\rho }_D^{(3)}$ saturates for ${\tau }^{-1}\gg T/{\alpha }^2$).

Figure 3

Schematic view of the drag coefficient at low temperatures. Left: ${\rho }_D^{(2)}(\mu )$ (solid line) and ${\rho }_D^{(3)}(\mu )$ (blue dashed line). The arrows indicate the tendency of the two terms with the decrease of temperature $T\to 0$. Right: ${\rho }_D^{(3)}(\mu =0)$ and ${\rho }_D^{\mathrm{corr}}(\mu =0)$ (solid line) as functions of $T$ [26].