Letter | Published:

Exploring 4D quantum Hall physics with a 2D topological charge pump

Nature volume 553, pages 5558 (04 January 2018) | Download Citation

Abstract

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect1: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field2. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number3,4. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect5,6. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted4.

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Acknowledgements

We acknowledge discussions with M. Aidelsburger and I. Carusotto. This work was funded by the European Commission (UQUAM, SIQS), the Deutsche Forschungsgemeinschaft (DIP, FOR2414) and the Nanosystems Initiative Munich. M.L. was additionally supported by the Elitenetzwerk Bayern (ExQM), H.M.P. by the European Commission (FET Proactive, grant no. 640800 ‘AQuS’, and Marie Skłodowska–Curie Action, grant no. 656093 ‘SynOptic’) and the Autonomous Province of Trento (SiQuro), and O.Z. by the Swiss National Science Foundation.

Author information

Affiliations

  1. Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstraße 4, 80799 München, Germany

    • Michael Lohse
    • , Christian Schweizer
    •  & Immanuel Bloch
  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany

    • Michael Lohse
    • , Christian Schweizer
    •  & Immanuel Bloch
  3. INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, Via Sommarive 14, 38123 Povo, Italy

    • Hannah M. Price
  4. School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

    • Hannah M. Price
  5. Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Straße 27, 8093 Zürich, Switzerland

    • Oded Zilberberg

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Contributions

M.L. and C.S. performed the experiment and data analysis. O.Z. proposed the experiment. All authors contributed to the theoretical analysis and to writing the paper. I.B. supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Immanuel Bloch.

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https://doi.org/10.1038/nature25000

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