Topological polarization in disordered systems

TL;DR

This paper rigorously derives the King-Smith and Vanderbilt formula for orbital polarization, extending its applicability to disordered and continuous random systems in piezoelectric materials.

Contribution

It provides a rigorous mathematical derivation of the orbital polarization formula applicable to generalized disordered systems.

Findings

Derived a generalized formula for orbital polarization

Extended the formula's applicability to disordered systems

Provided mathematical rigor to existing physical theories

Abstract

Deformations in piezoelectric materials lead to conduction effects, which are due to two contributions: the relative displacements of the ionic cores, and the so-called orbital polarization. This work is devoted to the rigorous derivation of the celebrated King-Smith and Vanderbilt formula for orbital polarization in a generalized setting that includes continuous random systems among others.