Current-Density Functional Theory of the Response of Solids

TL;DR

This paper develops a current-density functional theory approach to accurately describe the response of solids to homogeneous fields, addressing limitations of traditional TDDFT by incorporating macroscopic current effects.

Contribution

It introduces a current-density functional theory framework that captures the macroscopic current response in solids, which is absent in standard TDDFT.

Findings

Identifies the failure of TDDFT for homogeneous fields in solids.

Derives a formally exact polarization functional in the low-frequency limit.

Highlights the importance of macroscopic current in response calculations.

Abstract

The response of an extended periodic system to a homogeneous field (of wave-vector $q=0$) cannot be obtained from a $q=0$ time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply. Time-dependent {\em current}-density functional theory is needed and demonstrates that one key ingredient missing from TDDFT is the macroscopic current. In the low-frequency limit, in certain cases, density polarization functional theory is recovered and a formally exact expression for the polarization functional is given.