Hall conductivity pump

TL;DR

This paper introduces a topological invariant for quantifying the pump of Hall conductance in three-dimensional materials, extending the concept of charge pumping from one-dimensional systems.

Contribution

It proposes a novel topological invariant that measures Hall conductance pumping in 3D materials, expanding the theoretical framework of topological charge pumps.

Findings

Defines a topological invariant for 3D Hall conductance pump

Extends the concept of charge pumping to three-dimensional systems

Provides a theoretical basis for future experimental exploration

Abstract

The Thouless charge pump represents a transfer of electric charge through a gapped one-dimensional system between its zero-dimensional boundaries under a periodic change of a parameter. The value of the passed charged during a single cycle is known to be a topological invariant. We construct an analogous topological invariant that measures a pump of Hall conductance inside of three-dimensional material between its two-dimensional boundaries.