Variable-range-hopping magnetoresistance

Publisher Website
Google Scholar
Abstract
The hopping magnetoresistance R of a two-dimensional insulator with metallic impurities is considered. In sufficiently weak magnetic fields it increases or decreases depending on the impurity density n: It decreases if n is low and increases if n is high. In high magnetic fields B, it always exponentially increases with √B . Such fields yield a one-dimensional temperature dependence: lnR∝1/ √T . The calculation provides an accurate leading approximation for small impurities with one eigenstate in their potential well. In the limit of infinitesimally small impurities, an impurity potential is described by a generalized function. This function, similar to a δ function, is localized at a point, but, contrary to a δ function in the dimensionality above 1, it has finite eigenenergies. Such functions may be helpful in the study of scattering and localization of any waves.