Exact density-functional potentials for time-dependent quasiparticles

TL;DR

This paper derives the exact time-dependent Kohn-Sham potential for a quasiparticle in a semiconductor, revealing complex nonlocal dependencies crucial for accurate density-functional theory simulations.

Contribution

It provides the first exact calculation of the time-dependent Kohn-Sham potential for a quasiparticle, highlighting nonlocal and non-adiabatic features.

Findings

The potential exhibits highly nonlocal functional dependence on charge density.

Non-equilibrium Kohn-Sham electric field depends on local current and charge density.

Features differ significantly from local or adiabatic approximations.

Abstract

We calculate the exact Kohn-Sham potential that describes, within time-dependent density-functional theory, the propagation of an electron quasiparticle wavepacket of non-zero crystal momentum added to a ground-state model semiconductor. The potential is observed to have a highly nonlocal functional dependence on the charge density, in both space and time, giving rise to features entirely lacking in local or adiabatic approximations. The dependence of the non-equilibrium part of the Kohn-Sham electric field on the local current and charge density is identified as a key element of the correct Kohn-Sham functional.