Thouless pumping and topology

By R. Citro, M. Aidelsburger. Nature Reviews Physics, 2022

189 citations recorded by the source corpus.

Thouless pumping is a dynamical quantum effect that results in a quantized response of a many-body system. It stems from the topological properties of the band structure that emerge under a periodic drive in the adiabatic limit. This Review addresses the robustness of topology in adiabatically driven systems exploring fundamental issues regarding the roles of interactions, disorder and higher dimensions in quantum transport. 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. A direct current is usually associated with a dissipative flow of electrons in response to an applied bias voltage. In quantum systems, however, coherent transport can be induced via adiabatic cyclic variation of at least two system parameters in the absence of any external bias. A Thouless pump is a ‘quantum’ pump, in which the amount of ‘charge’ pumped during one cycle is quantized according to the Chern number — a topological invariant. Quantized charge pumps are robust to perturbations, such as disorder or weak interactions, as long as they do not change the topology of the pump. One-dimensional topological pumps can be seen as dynamical versions of the 2D integer quantum Hall effect in (1+1)-D, in which time plays the role of one spatial dimension and can be understood as a synthetic dimension. The concept of synthetic dimensions opens the door towards realizations of exotic higher-dimensional systems, such as the 4D quantum Hall effect.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/753573415c9ecb9e448ea0a237d7d6f7b47b9d31