Honeycomb optical lattices with harmonic confinement

Abstract

We consider the fate of the Dirac points in the spectrum of a honeycomb optical lattice in the presence of a harmonic confining potential. By numerically solving the tight binding model we calculate the density of states, and find that the energy dependence can be understood from analytical arguments. In addition, we show that the density of states of the harmonically trapped lattice system can be understood by application of a local density approximation based on the density of states of the homogeneous lattice. The Dirac points are found to survive locally in the trap as evidenced by the local density of states. They furthermore give rise to a distinct spatial profile of a noninteracting Fermi gas.

8 pages, 6 figures

References in corpus (31)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Synthetic magnetic fields for ultracold neutral atoms
• Production of cold molecules via magnetically tunable Feshbach resonances
• Bragg spectroscopy of a Bose-Einstein condensate
• Graphene: new bridge between condensed matter physics and quantum electrodynamics
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Coherent transport of neutral atoms in spin-dependent optical lattice potentials
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Momentum-Resolved Bragg Spectroscopy in Optical Lattices
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Ultracold Fermions in a Graphene-Type Optical Lattice
• The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
• Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
• Topological Insulators and Metals in Atomic Optical Lattices
• Topological phase transitions in the non-Abelian honeycomb lattice
• Massless Dirac Fermions in a Square Optical Lattice
• Wannier states and Bose-Hubbard parameters for 2D optical lattices
• Single-atom density of states of an optical lattice
• Confinement control by optical lattices
• Radio Frequency Selective Addressing of Localized Particles in a Periodic Potential
• Efficient and robust initialization of a qubit register with fermionic atoms
• Finite temperature theory of superfluid bosons in optical lattices

Cited by in corpus (9)

• Topological quantum matter with cold atoms
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
• Relativistic quantum effects of Dirac particles simulated by ultracold atoms
• Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
• The nonlinear Dirac equation in Bose-Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices
• The nonlinear Dirac equation in Bose-Einstein condensates: Vortex solutions and spectra in a weak harmonic trap
• The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices