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arXiv:0712.4284 · Physical Review B

p x , y -orbital counterpart of graphene: Cold atoms in the honeycomb optical lattice

Congjun Wu, S. Das Sarma

Published Jun 11, 2008• 218 citations
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Abstract

We study the ground-state properties of the interacting spinless fermions in the ${p}_{x,y}$-orbital bands in the two-dimensional honeycomb optical lattice, which exhibit different features from those in the ${p}_{z}$-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 $n=\frac{i}{6}(i=1--6)$. At $n=\frac{1}{6}$, 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 $n=\frac{1}{2}$ and $\frac{5}{6}$, and the latter case is accompanied with the charge-density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at $n=\frac{1}{3},\frac{2}{3}$. These crystalline orders exhibit themselves in the noise correlations of the time-of-flight spectra.

DOI
10.1103/physrevb.77.235107

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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.
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter t0{t}_{0}t0​ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.
We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical lattice. The system allows an exact determination of the Green function, hence of the transport properties. The inter-species interaction can be tuned via the interplay between scattering length and confinements. Band structure and density of states of a periodic lattice are derived for different values of the interaction strength. Emergence and features of Dirac cones are pointed out, together with the appearance of multiple gaps and a non-dispersive and isolated flat band. Robustness against finite-size and vacancies effects is numerically investigated.
The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
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.