Measuring topology in a laser-coupled honeycomb lattice: from Chern insulators to topological semi-metals

Abstract : Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model (1988 Phys. Rev. Lett. 61 2015). In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e. a non-zero Chern number. In this paper, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldane's original model.
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New Journal of Physics, Institute of Physics: Open Access Journals, 2013, 15, pp.013025. 〈10.1088/1367-2630/15/1/013025〉
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N Goldman, E Anisimovas, F Gerbier, P Öhberg, I B Spielman, et al.. Measuring topology in a laser-coupled honeycomb lattice: from Chern insulators to topological semi-metals. New Journal of Physics, Institute of Physics: Open Access Journals, 2013, 15, pp.013025. 〈10.1088/1367-2630/15/1/013025〉. 〈hal-01587047〉

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