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

P. Bogdanski·H. Ouerdane
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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.

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P. Bogdanski, H. Ouerdane. 2006-10-31. Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory. https://doi.org/10.1103/physrevb.74.085210

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