Fractional quantization of the topological charge pumping in a one-dimensional superlattice

TL;DR

This paper demonstrates that under certain symmetries, fractional parts of a 1D topological charge pump transfer quantized charge, revealing a new fractional quantization phenomenon in topological systems.

Contribution

It introduces the concept of fractional quantization in topological charge pumping under symmetry conditions, extending the understanding of topological invariants in 1D systems.

Findings

Fractional quantization occurs at specific fractions of the pumping period.

Quantization is independent of boundary conditions.

Relevance for cold atomic gases in optical superlattices.

Abstract

A one-dimensional quantum charge pump transfers a quantized charge in each pumping cycle. This quantization is topologically robust being analogous to the quantum Hall effect. The charge transferred in a fraction of the pumping period is instead generally unquantized. We show, however, that with specific symmetries in parameter space the charge transferred at well-defined fractions of the pumping period is quantized as integer fractions of the Chern number. We illustrate this in a one-dimensional Harper-Hofstadter model and show that the fractional quantization of the topological charge pumping is independent of the specific boundary conditions taken into account. We further discuss the relevance of this phenomenon for cold atomic gases in optical superlattices.