Tight binding models for ultracold atoms in honeycomb optical lattices

Abstract

We discuss how to construct tight-binding models for ultra cold atoms in honeycomb potentials, by means of the maximally localized Wannier functions (MLWFs) for composite bands introduced by Marzari and Vanderbilt [1]. In particular, we work out the model with up to third-nearest neighbors, and provide explicit calculations of the MLWFs and of the tunneling coefficients for the graphene-lyke potential with two degenerate minima per unit cell. Finally, we discuss the degree of accuracy in reproducing the exact Bloch spectrum of different tight-binding approximations, in a range of typical experimental parameters.

5 pages, 5figures

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• Driving protocol for a Floquet topological phase without static counterpart
• The eight-fold way for optical quasicrystals
• Quantum phases in tunable state-dependent hexagonal optical lattices
• Construction of real-valued localized composite Wannier functions for insulators
• Zitterbewegung of moiré excitons in twisted MoS${}_2$/WSe${}_2$ hetero-bilayers
• The Higgs mode in a superfluid of Dirac fermions
• Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices
• Two-Dimensional Bose-Hubbard Model for Helium on Graphene
• Breakdown of the Peierls substitution for the Haldane model with ultracold atoms
• Wannier functions using a discrete variable representation for optical lattices
• Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands
• Shift photoconductivity in the Haldane model
• Hubbard parameters for programmable tweezer arrays
• Path integral Monte Carlo on a lattice: extended states
• Ab initio analysis of the topological phase diagram of the Haldane model
• Localization of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects
• Correspondence between a shaken honeycomb lattice and the Haldane model
• Bilayer honeycomb lattice with ultracold atoms: Multiple Fermi surfaces and incommensurate spin density wave instability
• Dynamical freezing and switching in periodically driven bilayer graphene
• Topological Phase Diagram of Optimally Shaken Honeycomb Lattices: A Dual Perspective from Stroboscopic and Non-Stroboscopic Floquet Hamiltonians
• Viscous dissipation in a gas of one-dimensional fermions with generic dispersion
• An eight-fold optical quasicrystal with cold atoms