Negative Coulomb Drag in Double Bilayer Graphene

We report on an experimental measurement of Coulomb drag in a double quantum well structure consisting of bilayer-bilayer graphene, separated by few layer hexagonal boron nitride. At low temperatures and intermediate densities, a novel negative drag response with an inverse sign is observed, distinct from the momentum and energy drag mechanisms previously reported in double monolayer graphene. By varying the device aspect ratio, the negative drag component is suppressed and a response consistent with pure momentum drag is recovered. In the momentum drag dominated regime, excellent quantitative agreement with the density and temperature dependence predicted for double bilayer graphene is found.

Figure 1

Coulomb drag. (a) Schematic of a double bilayer graphene device and local Coulomb drag measurement. (Left inset) Optical image of a double bilayer graphene device. (Right inset) Cross section of the bilayer graphene-hBN heterostructure. (b) $R_{\text{drag}}$ as a function of $n_T$ and $n_B$ at 300 K from the local drag measurement. The solid curves are isolevels. (Inset) The behavior of $R_{\text{drag}}$ at 300 K along match density lines, $n_T=n_B$ ($e\text{−}e$) and $n_T=-n_B$ ($e\text{−}h$).

Figure 2

Negative drag. (a) $R_{\text{drag}}$ as a function of top and bottom layer density, $n_T$ and $n_B$, respectively, at 120 K. (b) $R_{\text{drag}}$ along the matched density line, $n_T=\pm n_B$. (c) Drive layer resistivity along the same density line. The approximate charge puddle regime, defined by the full width at half maximum (FWHM) of the resistivity peak, is shown as the grey shaded area. (Left inset) The temperature dependence of $R_{\text{drag}}$ at select densities along the $n_T=-n_B$. (Right inset) $R_{\text{drag}}$ under the equal density condition, $n_T=-n_B$, at varying temperatures. The yellow solid line marks the FWHM of the drive layer resistivity peak at varying temperatures.

Figure 3

Local and nonlocal drag. (a) Schematic of the local and nonlocal drag measurement. (b) Density dependence of $R_{\text{drag}}$ from a local geometry measured at 140 K (upper panel). Density dependence of $R_{\text{drag}}$ from a nonlocal geometry measured at 140 K (lower panel). (c) Temperature dependence of $R_{\text{drag}}$ under the equal density condition $n_T=-n_B=7\times {10}^{11}{\mathrm{cm}}^{-2}$, taken from local and nonlocal measurements. The black dashed line corresponds to the expected $T^2$ dependence, and the dash-dotted line is a fit to the local measurement. (Inset) The value of $\beta$ versus the geometric factor $w/L$, where $\beta$ is obtained by fitting $R_{\text{drag}}$ with a power law temperature dependence. (d) $R_{\text{drag}}$ versus inverse density in the matched density regime, $n_T=n_B$, from the local and nonlocal measurement at $T=150\mathrm{K}$. The dashed lines are fits to $R_{\text{drag}}$ with a power law density dependence. The fit coefficient $\alpha$ is plotted in the inset against the geometric factor $w/L$.

Figure 4

Magnetodrag. (a) $R_{\text{drag}}$ measured at $T=200$ and 70 K, $B=1\mathrm{T}$ as a function of the match density, and $n_T=n_B$. The density dependence of $R_{\text{drag}}$ at (lower left inset) 200 K and (lower right inset) 70 K. (b) Hall drag $R_{xy}$ measured at $T=200$ and 70 K, $B=1\mathrm{T}$ as a function of match density, and $n_T=n_B$. The density dependence of $R_{xy}$ measured at (lower left inset) $T=200\mathrm{K}$ and (lower right inset) 70 K.