Lifshitz model in the presence of spin–orbit coupling

Abstract

Wave function of a localized state created by a short-range impurity in two dimensions falls off with distance, r, from the impurity as 1r1/2exp(−ra), where a is the localization radius. With randomly positioned identical impurities with low concentration, n≪a−2, the level smears into a band due to the overlap of the impurity wave functions. This is the essence of the Lifshitz model. We demonstrate that, upon incorporation of the spin–orbit coupling, the impurity wave functions acquire oscillating factors which, subsequently, modify their overlap. As a result of such modification, the density of states develops singularities at certain energies.