Thouless pumping and topology

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 David Thouless and Qian Niu in 1983 and 1984, it has been 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 long been 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 in bosonic systems. Recent experimental studies have been performed in diverse platforms ranging from cold atoms to photonics and condensed-matter systems. This Review serves as a basis to understand the robustness of the topology of slowly driven systems and also highlights the rich properties of topological pumps and their diverse range of applications. Examples include systems with synthetic dimensions or work towards understanding higher-order topological phases, which underline the relevance of topological pumping for the fast-growing field of topological quantum matter.

Automated summary

Thouless pumping is a simple manifestation of topology in quantum systems that has attracted much interest in recent years. The quantization of the pumped charge has been argued to be robust against weak disorder, but the localization properties of relevant states and the breakdown of quantized transport in the presence of interaction or out of the adiabatic approximation have been debated. Thouless pumping is the first example of a topological phase in a driven system, and recent experimental studies have been conducted in various platforms. This Review provides a basis for understanding the robustness of topology in slowly driven systems and highlights the rich properties and applications of topological pumps.