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 [Phys. Rev. Lett. 61, 2015 (1988)]. 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 work, 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.

30 pages, 12 figures, 4 Appendices

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Cited by in corpus (12)

• Direct imaging of topological edge states in cold-atom systems
• Periodically-driven quantum matter: the case of resonant modulations
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Phase spectroscopy of topological invariants in photonic crystals
• Direct Probe of Topological Order for Cold Atoms
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Identifying topological edge states in 2D optical lattices using light scattering
• Moving and merging of Dirac points on a square lattice and hidden symmetry protection
• Generating topological optical flux lattices for ultracold atoms by modulated Raman and radio-frequency couplings
• Metal-insulator phase transition and topology in a three-component system
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes