Time-dependent density-functional theory for ultrafast interband excitations

TL;DR

This paper develops a time-dependent density functional theory framework for analyzing ultrafast interband excitations in semiconductors, capturing many-body effects and excitonic features in optical spectra.

Contribution

It introduces a TDDFT formulation based on the density matrix, deriving semiconductor Bloch equations that include many-body effects exactly.

Findings

Optical absorption spectra show excitonic features with Coulomb singularity.

Qualitative agreement with Hartree-Fock results.

Framework applicable to ultrafast phenomena in semiconductors.

Abstract

We formulate a time-dependent density functional theory (TDDFT) in terms of the density matrix to study ultrafast phenomena in semiconductor structures. A system of equations for the density matrix components, which is equivalent to the time-dependent Kohn-Sham equation, is derived. From this we obtain a TDDFT version of the semiconductor Bloch equations, where the electronic many-body effects are taken into account in principle exactly. As an example, we study the optical response of a three-dimensional two-band insulator to an external short-time pulsed laser field. We show that the optical absorption spectrum acquires excitonic features when the exchange-correlation potential contains a $1/q^{2}$ Coulomb singularity. A qualitative comparison of the TDDFT optical absorption spectra with the corresponding results obtained within the Hartree-Fock approximation is made.