Frictional Magneto-Coulomb Drag in Graphene Double-Layer Heterostructures

Coulomb interaction between two closely spaced parallel layers of conductors can generate the frictional drag effect by interlayer Coulomb scattering. Employing graphene double layers separated by few‐layer hexagonal boron nitride, we investigate density tunable magneto- and Hall drag under strong magnetic fields. The observed large magnetodrag and Hall-drag signals can be related with Laudau level filling status of the drive and drag layers. We find that the sign and magnitude of the drag resistivity tensor can be quantitatively correlated to the variation of magnetoresistivity tensors in the drive and drag layers, confirming a theoretical formula for magnetodrag in the quantum Hall regime. The observed weak temperature dependence and $\sim B^2$ dependence of the magnetodrag are qualitatively explained by Coulomb scattering phase-space argument.

Figure 1

(a) Magnetodrag resistance as a function of top gate ($V_{\mathrm{TG}}$) and bottom gate voltages($V_{\mathrm{BG}}$), measured under a magnetic field of 1 T and at a temperature of 70 K. Black and green dashed lines mark charge neutrality and $\nu =2$ of the individual layers, respectively. The lower inset shows the drag resistance at zero magnetic field and a higher temperature of 300 K. (b) Hall-drag resistance under the same condition as (a). The upper insert shows the measurement schematics of the experiment. The lower inset shows an optical microscope image of the device used in this experiment.

Figure 2

(a),(b) Measured magneto- and Hall-drag resistivity at $T=70\mathrm{K}$, $B=13\mathrm{T}$. (c),(d) Calculated magneto- and Hall-drag resistivity using Eq. (1). The calculation is in arbitrary units (a.u.) due to the undetermined prefactor. The black dashed lines in (a)–(d) are charge neutrality lines of top and bottom layers. And the green outlined regions mark the ${\nu }_{\mathrm{top}}=2$ incompressible strip. (e),(f) Magnetoresistivity of top and bottom layers at $T=70\mathrm{K}$, $B=13\mathrm{T}$. (g),(h) Hall resistivity of top and bottom layers under the same condition. (i) Line cut of measured and calculated magneto- and Hall drag along the equal-density line ($n_T=n_B$). The dashed vertical line around $V_{\mathrm{BG}}\approx 10\mathrm{V}$ separates the first LL ($N=1$) region (right) from the zeroth LL ($N=0$) region (left). In the first LL region, measured drag is multiplied by a factor 26 for clarity, while the calculation is multiplied by a factor 20 in order to make a good comparison to the measured values.

Figure 3

(a) Magnetodrag along equal density line ($n_B=n_T$) as a function of densities at $B=13\mathrm{T}$ and different temperatures. The blue (yellow) shaded region marks $N=\pm 1$ ($N=0$) LL. The drag signals are multiplied by a factor of 20 in the blue shaded regions for clarity. (b) Drag as a function of temperature at different density points. Solid lines represent the Landau gaps $\nu =\pm 2$. Dashed line represents partially filled LLs $n=-1.6$, $2\times 10^{11}{\mathrm{cm}}^{-2}$, corresponding to $N=0$ LL and $n=-11\times 10^{11}{\mathrm{cm}}^{-2}$, corresponding to $N=-1$ LL. The density of each line in (b) is marked out in (a) by arrows with corresponding colors. (c) Magnetodrag as a function of the field at a temperature of 240 K at certain density points along equal density line (shown as * in the insert). Circles are experimental data, and solid curves are quadratic fits of the data.