Linear Magnetoresistance in a Quasifree Two-Dimensional Electron Gas in an Ultrahigh Mobility GaAs Quantum Well

We report a high-field magnetotransport study of an ultrahigh mobility ($\overline{\mu }\approx 25\times 10^6{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$) $n$-type GaAs quantum well. We observe a strikingly large linear magnetoresistance (LMR) up to 33 T with a magnitude of order ${10}^5\%$ onto which quantum oscillations become superimposed in the quantum Hall regime at low temperature. LMR is very often invoked as evidence for exotic quasiparticles in new materials such as the topological semimetals, though its origin remains controversial. The observation of such a LMR in the “simplest system”—with a free electronlike band structure and a nearly defect-free environment—excludes most of the possible exotic explanations for the appearance of a LMR and rather points to density fluctuations as the primary origin of the phenomenon. Both, the featureless LMR at high $T$ and the quantum oscillations at low $T$ follow the empirical resistance rule which states that the longitudinal conductance is directly related to the derivative of the transversal (Hall) conductance multiplied by the magnetic field and a constant factor $\alpha$ that remains unchanged over the entire temperature range. Only at low temperatures, small deviations from this resistance rule are observed beyond $\nu =1$ that likely originate from a different transport mechanism for the composite fermions.

Figure 1

(a) Longitudinal (black) and Hall resistance (red) at 0.3 K. The blue arrows indicate from left to right the positions of the filling factors $\nu =2$, 1 and $1/2$, respectively. (b) Drude mobility as calculated from the sheet resistance at zero magnetic field. (c) Longitudinal resistance curves in a temperature range from 20 K to 80 K. Different temperatures are indicated by different colors and are offset by a constant value of $500\mathrm{\Omega }$ for clarity. The inset shows a schematic of the sample dimensions.

Figure 2

(a) Longitudinal resistance $R_{\mathrm{xx}}$ (black curve) and calculated resistance rule $R_{\text{diff}}$ (red curve) for temperature of $T=0.3$, 1.2, 2.2, 10, and 20 K. For clarity the curves have been offset with respect to each other and the (blue) dashed lines indicate from left to right the positions of the filling factors $\nu =2$, 1 and $1/2$, respectively. (b) Magnification of the region around filling factor $\nu =1$ for low temperatures. The position of $\nu =1$ is indicated by the blue arrow. (c) Temperature dependence of the proportionality constant $\alpha$ as extracted from our data. The dashed lines show the spread of the data points.

Figure 3

Comparison of $R_{\mathrm{xy}}$ (black) and the inverted resistance rule $R_{\text{diff}}^{-1}$ (red) for 0.3 K, 1.2 K and 10 K. For clarity the curves have been offset with respect to each other. The blue arrows indicate from left to right the positions of the filling factors $\nu =2$, 1 and $1/2$, respectively.