Topological states in two-dimensional optical lattices

2009/12/31 by Tudor D. Stanescu, Victor Galitski, S. Das Sarma · 133 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Lattice (music) #Mathematics #Optical lattice #Physics #Quantum many-body systems #Quantum mechanics #Scattering #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #Ultracold atom #cond-mat.mes-hall #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1103/physreva.82.013608

published in Physical Review A 82(1) (American Physical Society) · 29 pages, 34 figures (references and new section added; published version)

arxiv created 2010/07/09 · openalex publication_date 2010/07/09 · arxiv updated 2010/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a general analysis of two-dimensional optical lattice models that give rise to topologically nontrivial insulating states. We identify the main ingredients of the lattice models that are responsible for the nontrivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multiorbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and, most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.

Citations

• One-Parameter Scaling at the Dirac Point in Graphene
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
• Quantum Spin Hall Effect in Graphene
• Topological Insulators with Inversion Symmetry
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Time-Reversal Symmetry Breaking by a (d+id) Density-Wave State in Underdoped Cuprate Superconductors
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Mean-field theory of spin-liquid states with finite energy gap and topological orders
• Quantum Criticality and Minimal Conductivity in Graphene with Long-Range Disorder
• Fractional Quantum Hall States of Atoms in Optical Lattices
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum anomalous Hall effect with cold atoms trapped in a square lattice
• Fault-tolerant quantum computation by anyons
• Nonequilibrium Spin Dynamics in a Trapped Fermi Gas with Effective Spin-Orbit Interactions

Cited by

• Chiral Rashba spin textures in ultracold Fermi gases
• An optical-lattice-based quantum simulator for relativistic field theories and topological insulators