Galilei covariance of the theory of Thouless pumps

TL;DR

This paper explores how the quantized charge transport in Thouless pumps transforms under Galilean symmetry, connecting different formalisms and applying the bulk-edge correspondence within scattering theory.

Contribution

It demonstrates the Galilei covariance of Thouless pumps and unifies various formalisms through a transformation of vector bundles and scattering theory.

Findings

Galilei covariance of Thouless pumps established

Different formalisms for charge transformation compared

Application of bulk-edge correspondence within scattering theory

Abstract

The Thouless theory of quantum pumps establishes the conditions for quantized particle transport per cycle, and determines its value. When describing the pump from a moving reference frame, transported and existing charges transform, though not independently. This transformation is inherent to Galilean space and time, but it is underpinned by a transformation of vector bundles. Different formalisms can be used to describe this transformation, including one based on Bloch theory. Depending on the chosen formalism, the two types of charges will be realized as indices of either the same or different kinds. Finally, we apply the bulk-edge correspondence principle, so as to implement the transformation law within B\"uttiker's scattering theory of quantum pumps.