Measurement of spin Chern numbers in quantum simulated topological insulators

Abstract

The topology of quantum systems has become a topic of great interest since the discovery of topological insulators. However, as a hallmark of the topological insulators, the spin Chern number has not yet been experimentally detected. The challenge to directly measure this topological invariant lies in the fact that this spin Chern number is defined based on artificially constructed wavefunctions. Here we experimentally mimic the celebrated Bernevig-Hughes-Zhang model with cold atoms, and then measure the spin Chern number with the linear response theory. We observe that, although the Chern number for each spin component is ill defined, the spin Chern number measured by their difference is still well defined when both energy and spin gaps are non-vanished.

arXiv comment12 pages, 9 figures

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• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
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• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
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• Observation of spin-tensor induced topological phase transitions of triply degenerate points with a trapped ion
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Dual topological insulator with mirror symmetry protected helical edge states
• Synthetic spin-orbit coupling for the multispin models in optical lattices
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
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• Corner Flat Bands Induced by $d$-Density Wave and Partial Corner State Modification Due to Competition with $d$-Wave Superconductivity
• Detecting degenerate bands topological invariants in optical lattice
• Proposal for realizing and probing topological crystalline insulators in optical lattices
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• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc