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Cited by 86Topological Materials and PhenomenaQuantum and electron transport phenomenaCold Atom Physics and Bose-Einstein Condensates

Measurement of Chern numbers through center-of-mass responses

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Price, H. M., Zilberberg, O., Ozawa, T., Carusotto, I., Goldman, N.·2016·Physical Review B
DOI 10.1103/physrevb.93.245113
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Abstract

The remarkable quantization of the Hall conductivity is routinely observed in two-dimensional electron gases subject to strong magnetic fields. Such quantum transport experiments are performed by measuring the current that flows in 2D systems in response to an applied electric field, and result in a quantized conductance proportional to a topological index, known as the Chern number. Recently, a similar effect was proposed and observed in gases of ultracold atoms, when these are loaded into Bloch bands with a nonzero Chern number. In this context, the center of mass of the atomic gas performs a measurable differential drift, in direct analogy with the electronic Hall effect, from which the corresponding Chern number can be obtained. Such detection relies on the assumption that the center-of-mass drift of the atomic cloud is directly related to the current density, which itself depends on the Chern number of the band. Here, the authors carefully revisit and analyze the center-of-mass detection scheme. Interestingly, we find that the center-of-mass motion also depends on the particle density, which in the presence of magnetic perturbations, can be explicitly related to the topology of the band. Whereas this additional dependence offers a correction to existing experimental results, it opens up a rich variety of new possible quantized responses and detection schemes in 2D and 4D engineered systems, such as cold atoms and photonic lattices.

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  • The model can be decomposed as a direct sum of 1D pumps that each have gaps associated with nontrivial 1st Chern numbers.

    “Since this model can be decomposed as a direct sum of 1D pumps that each have gaps that are associated with nontrivial 1 st Chern numbers 6,28,29 , it follows that:”

    From Photonic topological boundary pumping as a probe of 4D quantum Hall physics (2018) · cites this paper as [29]

    In “A. Minimal 4D topological model” (page unavailable), the paper describes the model as two constituent 2D Harper–Hofstadter models and identifies a first Chern number for each plane. Its discussion of Harper–Hofstadter gaps also associates gaps with Chern numbers of the bands below them. Our copy does not describe the decomposition as a direct sum of 1D pumps, so that part of the claim is not supported. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

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Authors
Price, H. M., Zilberberg, O., Ozawa, T., Carusotto, I., & Goldman, N.
Affiliations
  • University of Trento (IT)
  • ETH Zurich (CH)
  • Université Libre de Bruxelles (BE)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2016-06-06
Volume
93
Issue
24
ISSN
  • 2469-9950 (ISSN-L)
  • 2469-9969
DOI
10.1103/physrevb.93.245113
OpenAlex
W2262840273
Cited by
86
References
80
Citations by year
2026: 1 · 2025: 4 · 2024: 3 · 2023: 4 · 2022: 6 · 2021: 10 · 2020: 13 · 2019: 10 · 2018: 19 · 2017: 8 · 2016: 8
FWCI
7.09
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B./Physical review. B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • University of Birmingham Research Portal (University of Birmingham) (submittedVersion, other-oa)
  • Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
  • Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
  • European Research Council (640800)
  • European Commission (656093)
  • Fonds De La Recherche Scientifique - FNRS
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
Keywords
Chern number, ultracold atoms, topological band structure, quantum Hall effect, Hall conductivity quantization, Bloch bands, particle density dependence, magnetic disturbances, photonic lattices, topological quantization

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