Quasirelativistic electronic $T$-matrix for the short-range perturbation

TL;DR

This paper derives an exact quasirelativistic T-matrix for short-range delta-function perturbations in the Dirac equation, enabling analysis of bound and resonance states impacting transport in semiconductors.

Contribution

It provides a novel exact T-matrix solution for short-range perturbations in the Dirac equation using angular momentum separability.

Findings

Derived the exact T-matrix for delta-function perturbations.

Established a characteristic equation for bound and resonance states.

Applied results to transport properties in narrow-gap semiconductors.

Abstract

Exact $T$-matrix for the delta-function short-range perturbation of the (3+1)-Dirac equation has been derived. Separability of the potential in the angular momentum representation is used. A characteristic equation for the $T$-matric poles determining the bound and resonance states has been obtained. The calculated $T$-matrix determines transport properties of the narrow-gap and zero-gap semiconductors.