Thouless pumping and topology

TL;DR

This paper reviews Thouless pumping, a fundamental topological phenomenon in quantum systems, discussing its robustness, breakdown conditions, and applications in various platforms and emerging topological phases.

Contribution

It provides a comprehensive overview of the topological properties, robustness, and diverse applications of Thouless pumping in quantum systems and driven topological phases.

Findings

Quantized charge pumping is robust against weak disorder.

Breakdown occurs with strong interactions or non-adiabatic effects.

Thouless pumping enables exploration of higher-order and synthetic topological phases.

Abstract

Thouless pumping provides one of the simplest manifestations of topology in quantum systems, and has attracted a lot of recent interest, both theoretically and experimentally. Since the seminal works by Thouless and Niu in 1983 and 1984, it is argued that the quantization of the pumped charge is robust against weak disorder, but a clear characterization of the localization properties of the relevant states, and the breakdown of quantized transport in the presence of interaction or out of the adiabatic approximation, has been long debated. Thouless pumping is also the first example of a topological phase emerging in a periodically-driven system. Driven systems can exhibit exotic topological phases without any static analogue and have been the subject of many recent proposals both in fermionic and bosonic systems in diverse platforms ranging from cold atoms to photonics and condensed matter systems. In this respect, this review has a twofold purpose: On the one hand, it serves as a basis to understand the robustness of the topology of slowly-driven systems per se; On the other hand, it highlights the rich properties of topological pumps and their diverse range of applications, for instance, in systems with synthetic dimensions or for understanding higher-order topological phases. These examples underline the relevance of topological pumping for the fast growing field of topological quantum matter.