Linear magnetoresistance in a high quality two-dimensional electron system

In a high quality two-dimensional electron system of density $n \sim 1\times10^{11}$ cm$^{-2}$ and mobility $\mu \sim 10 \times10^6$ cm$^2$/Vs, at the temperature ($T$) of 1.2K, the diagonal magnetoresistance, $R_{xx}$, shows a strictly linear magnetic ($B$) field dependence, except for sharp spikes at $B$- fields where the integer quantum Hall effect develops. As $T$ is lowered to $\sim$ 35 mK, the main feature of $R_{xx}$ is now dominated by multiple minima and peaks, due to the formation of integer and fractional quantum Hall states. However, when plotting $R_{xx}$ at the even-denominator fillings ($\nu=1/4$, 1/2, 3/4, and 3/2) as a function of $B$ field, the same linear $B$ field dependence is recovered. Interestingly, this linear magnetoresistance cannot be understood under the composite fermion model. Rather, it can be explained in terms of a slight, unintentional electron density gradient in our sample: Practically all $R_{xx}$ features can be reproduced quantitatively through $R_{xy}$. We will discuss the implications of this finding.