An optimal topological spin pump

TL;DR

This paper investigates a ${ m Z}_2$ topological spin pump, revealing that nontrivial topological indices enable noiseless, quantized spin pumping without spin conservation, clarifying the ${ m Z}_2$ classification of certain insulators.

Contribution

It introduces a topological classification of ${ m Z}_2$ pumps based on scattering matrices and demonstrates their ability to pump quantized spin noiselessly.

Findings

Nontrivial topological index correlates with noiseless quantized spin pumping.

Topologically trivial pumps do not support quantized spin pumping.

The results clarify the ${ m Z}_2$ classification of time reversal invariant insulators.

Abstract

We study the recently introduced ${\mathbb Z}_2$ pump consisting of a family of one-dimensional bulk insulators with time reversal restriction on the pumping cycle. We find that the scattering matrices of these pumps are dichotomized by a topological index. We show that the class of pumps characterized by a nontrivial topological index allows, in contrast to its topologically trivial counterpart, for the noiseless pumping of quantized spin, even in the absence of spin conservation. This distinction sheds light on the ${\mathbb Z}_2$ classification of two-dimensional time reversal invariant insulators.