Lifshitz model in the presence of spin-orbit coupling

TL;DR

This paper investigates how spin-orbit coupling affects the Lifshitz model by altering impurity wave functions, leading to oscillations and resulting in singularities in the density of states at specific energies.

Contribution

It introduces the impact of spin-orbit coupling on impurity wave functions within the Lifshitz model, revealing new singularities in the density of states.

Findings

Impurity wave functions gain oscillating factors due to spin-orbit coupling.

Density of states develops singularities at specific energies.

Modification of wave function overlap affects the electronic properties.

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 r^{-1/2}exp(-r/a), 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.