Topological nature of polarization and charge pumping in ferroelectrics

TL;DR

This paper explores the topological aspects of polarization and charge pumping in ferroelectrics, linking the quantized charge transfer to the linking number of band-crossing trajectories in parameter space.

Contribution

It introduces a topological framework describing polarization and charge pumping using vector fields and linking numbers in parameter space, extending Thouless's quantization concept.

Findings

Charge pumping quantized by linking number

Vector field description of polarization

Topological interpretation of band-crossing trajectories

Abstract

Electric polarization or transferred charge due to an adiabatic change of external parameters $\vec{Q}$ is expressed in terms of a vector field defined in the $\vec{Q}$ space. This vector field is characterized by strings, i.e., trajectories of band-crossing points. In particular, the transverse component is given by the Biot-Savart law in a nonlocal way. For a cyclic change of $\vec{Q}$ along a loop C, the linking number between this string and C represents the amount of the pumped charge, which is quantized to be an integer as discussed by Thouless.