Energy-Driven Drag at Charge Neutrality in Graphene

Coulomb coupling in graphene heterostructures results in vertical energy transfer between electrons in proximal layers. We show that, in the presence of correlated density inhomogeneity in the layers, vertical energy transfer has a strong impact on lateral charge transport. In particular, for Coulomb drag, its contribution dominates over conventional momentum drag near zero doping. The dependence on doping and temperature, which is different for the two drag mechanisms, can be used to separate these mechanisms in experiments. We predict distinct features such as a peak at zero doping and a multiple sign reversal, which provide diagnostics for this new drag mechanism.

Figure 1

Different mechanisms for Coulomb drag in graphene heterostructures. The $E$ mechanism dominates over the $P$ mechanism near zero doping, whereas the $P$ mechanism dominates at higher doping. The sign of the drag response depends on carrier polarity (a). For potential fluctuations of equal sign in the two layers, Eq. (1), the net drag (b) features a pair of nodal lines (white dashed lines). Positive drag in the avoided crossing region at zero doping is dominated by the $E$ mechanism. The resulting dependence is distinct from $P$-mechanism-only drag (c) smeared by correlated density fluctuations, $\delta {\mu }_1\approx \delta {\mu }_2$.

Figure 2

Feynman diagrams for the $P$ mechanism (a) and the $E$ mechanism (b) for drag. Wavy lines represent interactions, dashed line represents disorder averaging. The ladder in (b) represents a long-wavelength charge-neutral mode.

Figure 3

(a) Total drag resistivity ${\rho }_{21}^{(\mathrm{tot})}={\rho }_{21}^{(m)}+{\rho }_{21}^{(e)}$ vs chemical potentials in the two layers, evaluated from Eqs. (11, 5) at $T=100\mathrm{K}$, producing a peak at ${\mu }_{1,2}=0$ (see text for parameter values used). (b, c) Slices ${\mu }_1={\mu }_2$ and ${\mu }_1=-{\mu }_2$ at different temperatures. Note a three-peak structure in panel (b) and two sign changes close to CN in (c). (d) Temperature dependence of the peak at ${\mu }_{1,2}=0$ in the diffusive regime.