Measurement of Chern numbers through center-of-mass responses

Year: 2016

Authors: Price HM., Zilberberg O., Ozawa T., Carusotto I., Goldman N.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy: Univ Trento, Dipartimento Fis, I-38123 Povo, Italy;‎ ETH, Inst Theoret Phys, CH-8093 Zurich, Switzerland; Univ Libre Bruxelles, Fac Sci, CENOLI, B-1050 Brussels, Belgium

Abstract: Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.

Journal/Review: PHYSICAL REVIEW B

Volume: 93 (24)      Pages from: 245113-1  to: 245113-16

KeyWords: QUANTIZED HALL CONDUCTANCE; TOPOLOGICAL EDGE STATES; MAGNETIC BLOCH BANDS; BERRY PHASE; THERMODYNAMIC DERIVATION; SEMICLASSICAL DYNAMICS; HOFSTADTER SPECTRUM; ULTRACOLD FERMIONS; FIELD; INSULATORS
DOI: 10.1103/PhysRevB.93.245113

Citations: 56
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