Plasmon-mediated Coulomb drag between graphene waveguides

We analyze theoretically charge transport in Coulomb coupled graphene waveguides (GWGs). The GWGs are defined using antidot lattices, and the lateral geometry bypasses many technological challenges of earlier designs. The drag resistivity ${\rho }_D$, which is a measure of the many-particle interactions between the GWGs, is computed for a range of temperatures and waveguide separations. It is demonstrated that for $T>0.1T_F$ the drag is significantly enhanced due to plasmons, and that in the low-temperature regime a complicated behavior may occur. In the weak coupling regime the dependence of drag on the interwaveguide separation $d$ follows ${\rho }_D\sim d^{-n}$, where $n\simeq 6$.

Figure 1

(a) Schematic illustration of a graphene waveguide (GWG): a region of pristine graphene of width $W$ sandwiched between regions of GALs. (b) Dispersion relation of GWG with $W=20$ nm; the black dotted line shows a representative Fermi level $E_F=0.054$ eV, which corresponds to the charge density $n\simeq 3\times {10}^{11}{\text{cm}}^{-2}$. (c) Coulomb drag setup: two parallel GWGs separated by the region of GAL of the width $d$.

Figure 2

(a) Drag resistivity between equal ballistic waveguides as a function of temperature for different chemical potentials. The width of the waveguides $W_1=W_2=20$ nm and $d=40$ nm. Nonlinear susceptibility at different (b) $T=5$ K and (c) $T=100$ K temperatures of the system and $E_F=0.050$ eV. (d), (e) Normalized drag intensity calculated using Eq. (14).

Figure 3

Drag resistivity as a function of temperature with unscreened (green solid line, the same as in Fig. 2) and screened (blue dashed line) Coulomb interaction. Pink dots on the curve correspond to the temperature points examined on (b) and (c). Inset: Low-temperature behavior of ${\rho }_D$. (b), (c) The nonlinear susceptibility calculated at different temperatures. Red curves show dispersion $\omega \left(q\right)$ of the plasmon modes. (d), (e) The normalized drag intensity.

Figure 4

Drag resistivity between two identical ($W_1=W_2=20$ nm) GWGs as a function of distance $d$ between them calculated at $T=0.085T_F$ (green line, left axis) and $T=0.15T_F$ (red line, right axis). The Fermi temperature is $T_F=580$ K and $k_F=0.0318$ 1/nm. The black dotted line illustrates asymptotic behavior in the regime $k_{F}d>1$.