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

Nature
Michael LohseI Bloch

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: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. 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. 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. 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 fi...Continue Reading

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May 22, 2018·Advanced Materials·Zhen GaoBaile Zhang
Jan 5, 2018·Nature·Oded ZilberbergMikael C Rechtsman
Jul 18, 2019·Nature Communications·Avik DuttShanhui Fan
Nov 24, 2018·Physical Review Letters·Xiao-Qi SunShanhui Fan
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