Microscopic Electronic Wavefunction and interactions between quasi particles in Empirical Tight-Binding Theory

TL;DR

This paper introduces a method to derive single-electron wavefunctions in tight-binding models, enabling detailed analysis of many-body effects like excitonic interactions in semiconductors.

Contribution

It presents a novel approach to obtain microscopic wavefunctions from tight-binding parameters, bridging the gap between empirical models and first-principles accuracy.

Findings

Wavefunctions agree well with first-principles calculations.

Method accurately predicts excitonic fine structure dispersion.

Enables modeling of many-body effects from tight-binding data.

Abstract

A procedure to obtain single-electron wavefunctions within the tight-binding formalism is proposed. It is based on linear combinations of Slater-type orbitals whose screening coefficients are extracted from the optical matrix elements of the tight-binding Hamiltonian. Bloch functions obtained for zinc-blende semiconductors in the extended-basis spds* tight-binding model demonstrate very good agreement with first-principles wavefunctions. We apply this method to the calculation of electron-hole exchange interaction, and obtain the dispersion of excitonic fine structure of bulk GaAs. Beyond semiconductor nanostructures, this work is a fundamental step toward modeling many-body effects from post-processing single particle wavefunctions within the tight-binding theory.