Jingjing Feng, UT-Austin

"Impurity Scattering of Electron in a Magnetic Field"

Abstract: Magneto-transport of two-dimensional electrons is an interesting but yet complicated topic in condensed matter physics. While most existing theories in magneto-transport are based on phase space Berry curvature, the mechanism of impurity scattering is less mentioned, but actually plays an important role in magneto-transport. Our theory focuses on how single electron-impurity scattering is influenced by electromagnetic field. In order to address the weak magnetic field problem, we consider two different regimes separately in transport: electron transport in weak magnetic field, electron transport in strong magnetic field. In order to address this difficulty, we introduce a new model recipe based on an abstraction of the actual impurity scattering process to redefine scattering parameters for the single elastic impurity scattering. It can introduce an appropriate set of scattering parameters in the presence of magnetic field to calculate the differential cross section. Specifically, the real scattering process can be abstracted into a sudden switch between the initial asymptotic and final asymptotic trajectory. Two effects emerges under this model: skew scattering and coordinate jump, which will eventually modify the Boltzmann equation. It results in anomalous Hall effect and Negative magnetoresistivity. In strong magnetic field, the electron motion can be generally described by the migration of guiding center. During the electron-impurity scattering, the guiding centers suddenly shift its coordinate. Traditionally, the electric field is not addressed in the impurity scattering process, but only in the drifting process. Because here we consider the electric field effect, the cyclotron radius changes in each individual scattering and the cumulative scattering broadens the cyclotron radius to be multiple values. At the same time, the coordinate shift accumulatively contribute to a longitudinal current due to the symmetry breaking of the energy spectrum by the electric field.