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arXiv:0905.1146 · Physical Review A

F -wave pairing of cold atoms in optical lattices

Wei-Cheng Lee, Congjun Wu, S. Das Sarma

Published Nov 10, 2010• 30 citations
arXivHTMLPDF

Abstract

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 $f$-wave pairing superfluidity of spinless fermions in ${p}_{x,y}$-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 $f$-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.

DOI
10.1103/physreva.82.053611

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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 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.
Geometric frustration in quantum magnetism refers to the fact that magnetic interactions on different bonds cannot be simultaneously minimized. The usual Cooper pairing systems favor uniform spatial distributions of pairing phases among different lattice sites without frustration. In contrast, we propose ``frustrated Cooper pairing'' in non-bipartite lattices which leads to supersolid states of Cooper pairs. Not only the amplitudes of the pairing order parameter but also its signs vary from site to site. This exotic pairing state naturally occurs in the ppp-orbital bands in optical lattices with ultracold spinless fermions. In the triangular lattice, it exhibits an unconventional supersolid state with the fff-wave symmetry.
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.
In this letter, we put forward another way for realizing topological superfluid (TS). In contrast to conventional method, spin-orbit coupling and external magnetic field are not requisite. Introducing an experimentally feasible technique called on-site rotation (OSR) into p-band honeycomb optical lattices for spinless Fermi gases and considering CDW and pairing on the same footing, we investigate the effects of OSR on superfluidity. The results suggest that when OSR is beyond a critical value, where CDW vanishes, the system transits from a normal superfluid (NS) with zero TKNN number to TS labeled by a non-zero TKNN number. In addition, phase transitions between different TSs are also possible.
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.
A Majorana zero bound mode exists in the vortex core of a chiral p+ipp+ipp+ip superconductor or superfluid, which can be driven from an sss-wave pairing state by two-dimensional spin-orbit coupling. We propose here a novel scheme based on realistic cold atom platforms to generate two-dimensional spin-orbit interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work may open a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.