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

Year: 2018

Authors: Lohse M., Schweizer C., Price HM., Zilberberg O., Bloch I.

Autors Affiliation: Ludwig Maximilians Univ Munchen, Fak Phys, Schellingstr 4, D-80799 Munich, Germany; Max Planck Inst Quantum Opt, Hans Kopfermann Str 1, D-85748 Garching, Germany; Univ Trento, INO CNR BEC Ctr, Via Sommarive 14, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, Via Sommarive 14, I-38123 Povo, Italy; Univ Birmingham, Sch Phys & Astron, Birmingham B15 2TT, W Midlands, England; ETH, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland.

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 effect(1): it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field(2). 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 number(3,4). 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 effect(5,6). 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 predicted(4).

Journal/Review: NATURE

Volume: 553 (7686)      Pages from: 55  to: +

More Information: 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 Sklodowska-Curie Action, grant no. 656093 ’SynOptic’) and the Autonomous Province of Trento (SiQuro), and O.Z. by the Swiss National Science Foundation.
KeyWords: Energy-spectrum; Magnetic Field; Edge States; Insulators; Transport; Electrons; Fermions; Phase; Spin
DOI: 10.1038/nature25000

Citations: 302
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