# Topological quantisation and gauge invariance of charge transport in liquid insulators

## TL;DR

This paper demonstrates that the electrical conductivity of insulating liquids can be rigorously expressed using integer atomic oxidation numbers, leveraging topological quantisation and gauge invariance, simplifying the description of charge transport.

## Contribution

It introduces a topological and gauge-invariant framework to represent charge transport in liquids using integer oxidation numbers instead of traditional Born charges.

## Key findings

- Electrical conductivity can be expressed via integer oxidation numbers.
- Topological quantisation ensures gauge invariance of charge transport.
- The approach simplifies the theoretical description of insulating liquids.

## Abstract

According to the Green-Kubo theory of linear response, the conductivity of an electronically gapped liquid can be expressed in terms of the time correlations of the adiabatic charge flux, which is determined by the atomic velocities and Born effective charges. We show that topological quantisation of adiabatic charge transport and gauge invariance of transport coefficients allow one to rigorously express the electrical conductivity of an insulating fluid in terms of integer-valued, scalar, and time-independent atomic oxidation numbers, instead of real-valued, tensor, and time-dependent Born charges.