Microscopic electronic wave function and interactions between quasiparticles in empirical tight-binding theory

A procedure to obtain single-electron wave functions 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 wave functions. We apply this method to the calculation of the electron-hole exchange interaction, and obtain the dispersion of excitonic fine structure in bulk GaAs. Beyond semiconductor nanostructures, this work is a fundamental step toward modeling many-body effects from post-processing single-particle wave functions within the tight-binding theory.