Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory

TL;DR

This paper introduces a method using variable phase theory to compute scattering states of holes in spherical bands affected by defects, considering strong spin-orbit coupling and finite-range potentials, with applications demonstrated through Yukawa potentials.

Contribution

It extends previous work by Ralph to include finite-range potentials and demonstrates the effectiveness of the variable phase method for calculating scattering phase shifts and amplitudes.

Findings

Variable phase method effectively computes scattering phase shifts.

Finite-range potentials are incorporated into the scattering analysis.

Applications to Yukawa potentials illustrate the method's utility.

Abstract

In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a semiconductor crystal. We follow a previous work done on this topic by Ralph [H. I. Ralph, Philips Res. Rept. 32 160 (1977)] to account for the p-wave nature and the coupling of valence band states. We extend Ralph's analysis to incorporate finite-range potentials in the scattering problem. We find that the variable phase method provides a very convenient framework for our purposes and show in detail how scattering amplitudes and phase shifts are obtained. The Green's matrix of the Schroedinger equation, the Lippmann-Schwinger equation and the Born approximation are also discussed. Examples are provided to illustrate our calculations with Yukawa type potentials.