open access publication

Article, 2023

Time-based Chern number in periodically driven systems in the adiabatic limit

Physical Review Research, ISSN 2643-1564, Volume 5, 1, Page 013081, 10.1103/physrevresearch.5.013081


Lu, I-Te 0000-0003-1649-7931 [1] Shin, Dong-Bin 0000-0001-8073-2954 [1] [2] De Giovannini, Umberto 0000-0002-4899-1304 [1] [3] Hübener, Hannes 0000-0003-0105-1427 [1] Zhang, Jin 0000-0001-7830-3464 [1] Latini, Simone 0000-0001-9553-5259 [1] [4] Rubio, Angel Secades 0000-0003-2060-3151 [1] [5]


  1. [1] Max Planck Institute for the Structure and Dynamics of Matter
  2. [NORA names: Germany; Europe, EU; OECD];
  3. [2] Gwangju Institute of Science and Technology
  4. [NORA names: South Korea; Asia, East; OECD];
  5. [3] University of Palermo
  6. [NORA names: Italy; Europe, EU; OECD];
  7. [4] Technical University of Denmark
  8. [NORA names: DTU Technical University of Denmark; University; Denmark; Europe, EU; Nordic; OECD];
  9. [5] Flatiron Institute
  10. [NORA names: United States; America, North; OECD]


To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic two-dimensional (2D) Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic 2D Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via how the parametric variable evolves in its own space. We justify our claims by investigating Thouless pumping in two one-dimensional (1D) tight-binding models, a three-site chain model, and a two-1D-sliding-chains model. The present findings could be extended to higher dimensions and other periodically driven configurations.


Chern, Chern number, Thouless pumping, adiabatic limit, chain model, claims, configuration, dimensions, findings, higher dimensions, invariance, limitations, model, momentum, momentum dimensions, number, one-dimensional (1D, parametric variables, pump, space, synthetic dimensions, synthetic two-dimensional, system, tight-binding model, topological invariants, topology, two-dimensional, variables


  • European Research Council
  • Deutsche Forschungsgemeinschaft
  • Simons Foundation
  • Alexander von Humboldt Foundation
  • European Commission

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