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arXiv:1009.2133 · Physical Review A

Quantum anomalous Hall states in the p -orbital honeycomb optical lattices

Machi Zhang, Hsiang-Hsuan Hung, Chuanwei Zhang, Congjun Wu

Published Feb 23, 2011• 58 citations
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Abstract

We study the quantum anomalous Hall states in the $p$-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.

DOI
10.1103/physreva.83.023615

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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 \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ, 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 propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental setups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.
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.
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.