Topology, oxidation states, and charge transport in ionic conductors

TL;DR

This paper reviews recent theoretical progress linking topological concepts with ionic charge transport, revealing that charge can be transported without ionic displacements and connecting these ideas to electron transfer theories.

Contribution

It introduces a topological framework for understanding ionic transport, including charge transport without ionic movement and its relation to electronic structure and electron transfer theories.

Findings

Charge can be transported without net ionic displacements.

A topological classification of ionic transport regimes.

Connections established between topological charge transport and Marcus-Hush electron transfer theory.

Abstract

Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge-invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport -- whereby each atom carries a well-defined integer charge -- with a rigorous quantum description of the electronic charge-density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper we review these progress and in particular that, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, we introduce a new connection between our topological picture and the well-known Marcus-Hush theory of electron transfer, which we are able to connect with the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. We finally report on a few recent applications to energy materials and planetary sciences.