Magnetoresistance from Guiding Center Drift of Two-Dimensional Electrons in a Smooth Disorder Potential

Linear magnetoresistance has been observed in a range of low-density, two-dimensional electron systems. For three-dimensional systems, linear magnetoresistance can be explained in terms of semiclassical drift of electrons in a smooth disorder potential. But as of yet there is no analogous theory for two-dimensional electron systems. Here we address this issue by studying the magnetoresistance of 2D electrons in a smooth random potential, as created, for example, by charged impurities in the substrate. In the presence of a sufficiently large magnetic field, electron trajectories experience a drift of their guiding centers along equipotential contours, in addition to the rapid cyclotron motion. Scattering from impurities or phonons allows electrons to hop from one equipotential contour to another, and at large enough magnetic field this process dominates their diffusion. We study the resulting electron diffusion constant, which determines the electrical resistance. Using scaling arguments and numerical simulations, we find regimes in which the magnetoresistance scales as B⁰, B^10/13, and B^10/7.