Thouless pumping and topology

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.

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References in corpus (23)

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• Reversal of quantised Hall drifts at non-interacting and interacting topological boundaries
• Interplay between disorder and topology in Thouless pumping on a superconducting quantum processor
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• Origins of electromagnetic radiation from spintronic terahertz emitters: A time-dependent density functional theory plus Jefimenko equations approach
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• Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion
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• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Charge and spin current pumping by ultrafast demagnetization dynamics
• Geometric Floquet theory
• Non-equilibrium phases of Fermi gas inside a cavity with imbalanced pumping
• High-order topological pumping on a superconducting quantum processor
• Deciphering the origin of spin current in spintronic terahertz emitters and its imprint on their electromagnetic radiation via time-dependent density functional theory
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• A hybrid quantum algorithm to detect conical intersections
• Inverse-designed dispersive time-varying nanostructures
• Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Charge and spin gaps of the ionic Hubbard model with density-dependent hopping
• Topological pumping induced by spatiotemporal modulation of interaction
• Splitting and connecting singlets in atomic quantum circuits
• Tutorial: From Topology to Hall Effects -- Implications of Berry Phase Physics
• Hall response in interacting bosonic and fermionic ladders
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Topological photon pumping in quantum optical systems
• Non-Adiabatic Effect in Topological and Interacting Charge Pumping
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Thouless pumping in Josephson junction arrays
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• Adiabatic charge transport in extended SSH models
• Autonomous Stabilization of Floquet States Using Static Dissipation
• Quantum transport phenomena induced by time-dependent fields
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Recent advances in the combination of nonlinearity and exceptional points
• The anomalous Floquet Anderson insulator in a continuously driven optical lattice
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Identification and properties of topological states in the bulk of quasicrystals
• Absence of disordered Thouless pumps at finite frequency
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• A symmetry-protected topological optical lattice clock
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Adiabatic charge transport through non-Bloch bands
• Quantization and quantum oscillations of the sublattice charge order in Dirac insulators
• Generalized Josephson effect with arbitrary periodicity in quantum magnets
• Quantum theory of fractional topological pumping of lattice solitons
• Quantized transport of solitons in Bose-Einstein condensates driven by spin-orbit coupling
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump
• Emergent topological properties in spatially modulated sub-wavelength barrier lattices
• Covariant formulation of the Berry connection in non-Hermitian systems
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach
• Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations
• Topological dynamics of adiabatic cat states
• Quantized Acoustoelectric Floquet Effect in Quantum Nanowires
• Galilei covariance of the theory of Thouless pumps
• Quantized transport of two-dimensional multifrequency solitons
• Topological anomalous Floquet photon pump
• A strong-driving toolkit for topological Floquet energy pumps with superconducting circuits
• Many-body localization in a slowly varying potential
• Anisotropy-driven topological quantum phase transition in magnetic impurities
• Optimal control over the full counting statistics in a non-adiabatic pump