Disorder-Induced Magnetoresistance in a Two-Dimensional Electron System

We predict and demonstrate that a disorder-induced carrier density inhomogeneity causes magnetoresistance (MR) in a two-dimensional electron system. Our experiments on graphene show a quadratic MR persisting far from the charge neutrality point. Effective medium calculations show that for charged impurity disorder, the low-field MR is a universal function of the ratio of carrier density to fluctuations in carrier density, a power law when this ratio is large, in excellent agreement with experiment. The MR is generic and should occur in other materials with large carrier density inhomogeneity.

Figure 1

In the upper panels, we show forces (apart from the drag force) and electron drift velocities in a sample with two regions of different charge carrier concentrations when there is no magnetic field. The bottom left (right) panel illustrates a region of higher (lower) carrier concentration than the sample average along with all the new forces that appear (apart from the change in drag force) when the magnetic field is applied. The change in drift velocity $\mathrm{\Delta }{v}_{\text{drift}}$ is against the direction of motion of the electron for both regions shown in the bottom panels and this is the microscopic origin of magnetoresistance.

Figure 2

Summary of the experimental results. (a) Conductivity as a function of carrier density $n$ (back-gate voltage $V_g$) at zero magnetic field for CVD-grown samples 1, 2, and 3, and the exfoliated graphene sample from [11]. (b) Longitudinal resistance $R_{xx}$ and Hall conductivity ${\sigma }_{xy}$ as a function of carrier density $n$ (back-gate voltage $V_g$) for CVD-grown samples 1, 2, and 3 and exfoliated sample at $T=4.2\mathrm{K}$ and $B=8\mathrm{T}$. Top and bottom horizontal scales apply to both (a) and (b). (c) Low field magnetoresistance of samples 1 (left), 2 (middle), and 3 (right). Data are open symbols taken at the carrier density indicated in legend. Solid lines are fits described in the text.

Figure 3

Theoretical and experimental results for the dependence of the coefficient of quadratic magnetoresistance (a) plotted as a function of the carrier density $n_0$ and gate voltage $V_g$ and (b) as a function of the ratio between carrier density $n_0$ and carrier density fluctuations $n_{\text{rms}}$. The predictions of the earlier theoretical models including the two-channel model by Ref. [8] and the area fraction effective medium theory by Ref. [10] are shown as solid lines. In both earlier models, the magnetoresistance vanishes quickly once $n_0>n_{\text{rms}}$. By contrast, the magnetoresistance discussed in this work persists away from the Dirac point. For $n\gg n_{\text{rms}}$, we find both theoretically and experimentally a power-law dependance: $A=(1/2)(n_0/n_{\text{rms}}{)}^{-2}$.