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arXiv:cond-mat/0701788 · Physical Review Letters

Flat Bands and Wigner Crystallization in the Honeycomb Optical Lattice

Congjun Wu, Doron L. Bergman, Leon Balents, S. Das Sarma

Published Aug 16, 2007• 548 citations
arXivHTMLPDF

Abstract

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.

DOI
10.1103/physrevlett.99.070401

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We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.
We study the ground-state properties of the interacting spinless fermions in the px,y{p}_{x,y}px,y​-orbital bands in the two-dimensional honeycomb optical lattice, which exhibit different features from those in the pz{p}_{z}pz​-orbital system of graphene. In addition to two dispersive bands with Dirac cones, the tight-binding band structure exhibits another two completely flat bands over the entire Brillouin zone. With the realistic sinusoidal optical potential, the flat bands acquire a finite but much smaller bandwidth compared to the dispersive bands. The band flatness dramatically enhanced interaction effects giving rise to various charge and bond ordered states at commensurate fillings of n=i6(i=1−−6)n=\frac{i}{6}(i=1--6)n=6i​(i=1−−6). At n=16n=\frac{1}{6}n=61​, the many-body ground states can be exactly solved as the close-packed hexagon states which can be stabilized even in the weakly interacting regime. The dimerization of bonding strength occurs at both n=12n=\frac{1}{2}n=21​ and 56\frac{5}{6}65​, and the latter case is accompanied with the charge-density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at n=13,23n=\frac{1}{3},\frac{2}{3}n=31​,32​. These crystalline orders exhibit themselves in the noise correlations of the time-of-flight spectra.
We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in (Büchler et al 2007 Nat. Phys. 3 726), such a system is described by an extended Bose–Hubbard model of hard-core bosons that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground-state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime and determine the stability of the crystalline phases towards strong two-body interactions.
The tremendous development of cold atom physics has opened up a whole new opportunity to study novel states of matter which are not easily accessible in solid-state systems. Here we propose to realize the fff-wave pairing superfluidity of spinless fermions in px,y{p}_{x,y}px,y​-orbital bands of two-dimensional honeycomb optical lattices. The nontrivial orbital band structure, rather than strong correlation effects, gives rise to the unconventional pairing with the nodal lines of the fff-wave symmetry. With a confining harmonic trap, zero-energy Andreev bound states appear around the circular boundary with a sixfold symmetry. The experimental realization and detection of this novel pairing state are feasible.
We study the Wigner crystallization on partially filled topological flat bands of kagome, honeycomb and checkerboard lattices. We identify the Wigner crystals (WCs) by analyzing the Cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength, measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The Wigner crystallization observed by us is a robust and general phenomenon, existing in all three lattice models for a broad range of filling factors and interaction parameters. The shape of the resulting WCs is determined by the boundary conditions of the chosen plaquette. It is to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.
We propose a scheme to realize the itinerant ferromagnetism of two-component cold fermionic atoms in the ppp-orbital bands in optical lattices. The band flatness in the two-dimensional honeycomb lattice dramatically amplifies the interaction effect, driving the ferromagnetic transition even with a relatively weak repulsive interaction. This scheme has the advantage that the stability of the system can be maintained without causing decay to the molecular state as one approaches the Feshbach resonance from the side with the positive scattering length. Experimental signatures and detections are also discussed.
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.