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Communications in Theoretical Physics

Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

Jing-Min Hou

Published Aug 1, 2009• 2 citations
Publisher

Abstract

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are chiral and show Berry's phase π when the wavevector adiabatically evolves along a closed circle. Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.

DOI
10.1088/0253-6102/52/2/11

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We study the quantum anomalous Hall states in the ppp-orbital bands of the honeycomb optical lattices loaded with single-component fermions. Such an effect has not yet been realized in both condensed-matter and cold-atom systems. By applying the available experimental techniques to rotate each lattice site around its own center, the band structures become topologically nontrivial. At a certain rotation angular velocity $\ensuremath{\Omega}$, a flat band structure appears with localized eigenstates carrying chiral current moments. By imposing the soft confining potential, the density profile exhibits a wedding-cake-shaped distribution with insulating plateaus at commensurate fillings. Moreover, the inhomogeneous confining potential induces dissipationless circulation currents, the magnitudes and chiralities of which vary with the distance from the trap center. In the insulating regions, the Hall conductances are quantized, and in the metallic regions, the directions and magnitudes of chiral currents can not be described by the usual local-density approximation. The quantum anomalous Hall effects are robust at temperature scales that are small compared to band gaps, which increase the feasibility of experimental realizations.
We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mott-insulator (MI), density wave (DW) and modulated superfluid (MS) phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.