Nonadiabatic Born effective charges in metals and the Drude weight

TL;DR

This paper extends the concept of Born effective charges to metals by introducing nonadiabatic effects, linking their sum to the Drude weight, and demonstrates this with first-principles calculations on several materials.

Contribution

It introduces a formalism for nonadiabatic Born effective charges in metals and relates their sum to the Drude weight, expanding the understanding of polarization in conductors.

Findings

Nonadiabatic Born effective charges are well-defined in metals.

The sum of these charges is proportional to the Drude weight.

Density functional perturbation theory confirms the formalism in specific materials.

Abstract

In insulators, Born effective charges describe the electrical polarization induced by the displacement of individual atomic sublattices. Such a physical property is at first sight irrelevant for metals and doped semiconductors, where the macroscopic polarization is ill-defined. Here we show that, in clean conductors, going beyond the adiabatic approximation results in nonadiabatic Born effective charges that are well defined in the low-frequency limit. In addition, we find that the sublattice sum of the nonadiabatic Born effective charges does not vanish as it does in the insulating case, but instead is proportional to the Drude weight. We demonstrate these formal results with density functional perturbation theory calculations of Al, and electron-doped SnS$_2$ and SrTiO$_3$.