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arXiv:1007.4637 · Physical Review A

Simulating and detecting the quantum spin Hall effect in the kagome optical lattice

Guocai Liu, Shi-Liang Zhu, Shao-Jian Jiang, Fadi Sun, W. M. Liu

Published Nov 4, 2010• 68 citations
arXivHTMLPDF

Abstract

We propose a model which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian in the kagome lattice and promises to host the transition from the quantum spin Hall insulator to the normal insulator. In addition, we design an experimental scheme to simulate and detect this transition in the ultracold atom system. The lattice intrinsic spin-orbit coupling is generated via the laser-induced-gauge-field method. Furthermore, we establish the connection between the spin Chern number and the spin-atomic density which enables us to detect the quantum spin Hall insulator directly by the standard density-profile technique used in atomic systems.

DOI
10.1103/physreva.82.053605

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We design an ingenious scheme to realize Haldane's quantum Hall model without Landau levels by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on site energies in two sublattices required in the model can be implemented through tuning the phase of one laser beam. The staggered magnetic field is generated from the light-induced Berry phase. Moreover, we establish a relation between the Hall conductivity and the atomic density, enabling us to detect the Chern number with the typical density-profile-measurement technique.
We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.
With ultracold atoms in an optical lattice, we propose an experimental scheme to simulate and detect the integer quantum Hall effect and a peculiar phase transition in a uniform magnetic field and an additional staggered magnetic field. The phase transition is characterized by the direct change from Hall plateau state $N\ensuremath{-}1$ to $\ensuremath{-}1$ due to Chern number redistribution when the staggered magnetic field is varied. We propose the possibility to observe the Hall conductivity and the phase transition by varying experimental parameters and measuring the number density of the ultracold atoms.
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.
We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.