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.

arXiv comment30 pages, 12 figures, 4 Appendices

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• Light-induced gauge fields for ultracold atoms
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Artificial gauge fields in materials and engineered systems
• Direct imaging of topological edge states in cold-atom systems
• Chiral Ladders and the Edges of Chern Insulators
• Quantum Quenches in Chern Insulators
• Floquet Topological States in Shaking Optical Lattices
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• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• The Realization and Dectection of Weyl Semimetals and Chiral Anomaly in Cold Atomic Systems
• Phase spectroscopy of topological invariants in photonic crystals
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Direct Probe of Topological Order for Cold Atoms
• Excitation band topology and edge matter waves in Bose-Einstein condensates in optical lattices
• Two-dimensional Chern semimetals on the Lieb lattice
• Three-level Haldane-like model on dice optical lattice
• Magnonic Analogs of Topological Dirac Semimetals
• Kibble-Zurek behavior in disordered Chern insulators
• Realising Haldane's vision for a Chern insulator in buckled lattices
• Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
• Detecting Majorana fermions in quasi-one-dimensional topological phases using nonlocal order parameters
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Identifying topological edge states in 2D optical lattices using light scattering
• Abelian Chern-Simons-Maxwell theory from a tight binding model of spinless fermions
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Design of laser-coupled honeycomb optical lattices supporting Chern insulators
• Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator
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• Moving and merging of Dirac points on a square lattice and hidden symmetry protection
• Predicting Large-Chern-Number Phases in a Shaken Optical Dice Lattice
• Non-Abelian Chern-Simons Theory from a Hubbard-like Model
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Slow quenches in Chern insulator ribbons
• Berry Curvature of interacting bosons in a honeycomb lattice
• Winding number order in the Haldane model with interactions
• Efficient algorithm to compute the Berry conductivity
• Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairings
• Topological order in the Haldane model with spin-spin on-site interactions
• 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
• Seeing Topological Order and Band Inversion in Optical Diatomic Chain