# Fractional quantization of charge and spin in topological quantum pumps

## TL;DR

This paper demonstrates the fractional quantization of spin transport in a topological spin pump, revealing novel topological phenomena arising from symmetries in a periodically modulated lattice system.

## Contribution

It introduces a spinfull generalization of the Harper-Hofstadter model showing fractional spin quantization linked to lattice symmetries.

## Key findings

- Fractional spin quantization occurs during specific fractions of the pumping cycle.
- The phenomenon is topological and depends on symmetries from the periodic field and lattice commensuration.
- The model extends understanding of topological charge and spin transport in quantum systems.

## Abstract

Topological quantum pumps are topologically equivalent to the quantum Hall state: In these systems, the charge pumped during each pumping cycle is quantized and coincides with the Chern invariant. However, differently from quantum Hall insulators, quantum pumps can exhibit novel phenomena such as the fractional quantization of the charge transport, as a consequence of their distinctive symmetries in parameter space. Here, we report the analogous fractional quantization of the spin transport in a topological spin pump realized in a one-dimensional lattice via a periodically modulated Zeeman field. In the proposed model, which is a spinfull generalization of the Harper-Hofstadter model, the amount of spin current pumped during well-defined fractions of the pumping cycle is quantized as fractions of the spin Chern number. This fractional quantization of spin is topological, and is a direct consequence of the additional symmetries ensuing from the commensuration of the periodic field with the underlying lattice.