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Physical Review A

Spin-based effects and transport properties of a spin-orbit-coupled hexagonal optical lattice

Guanyu Zhu, Qing‐Feng Sun, Y.-Y. Zhang, Kwok Sum Chan, W.-M. Liu, A.-C. Ji

Published Aug 13, 2013• 8 citations
Publisher

Abstract

We investigate an ultracold Fermi gas in a hexagonal lattice subjected to a strong Rashba spin-orbit coupling (SOC). We focus on the marginal Abelian limit with the strength of SOC $\ensuremath{\kappa}=\ensuremath{\pi}/2$, where the derived Dirac fermions are spin-1/2 spinors in contrast to the pure hexagonal lattice. We find a double-degeneracy at the center of the Brillouin zone, which is a spin-3/2 Dirac-Weyl fermion that can be represented as two spin-1/2 fermions. While at the corner of the Brillouin zone, there occur another two spin-1/2 fermions. These Dirac spinors display a verity of spin textures beyond the usual topological properties. Furthermore, we investigate the energy spectrum of one-dimensional (1D) zigzag and armchair ribbons, and show that the appearance of a new cone at the center of the Brillouin zone can induce two flat bands in a 1D zigzag ribbon. These unique properties allow us to transport a single spin-1/2 Dirac spinor through the 1D zigzag ribbon with two quasi-two-dimensional leads, where only the spin-up or spin-down freedom of the Dirac spinors can transit through the ribbon.

DOI
10.1103/physreva.88.023608

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We investigate an ultracold Fermi gas in a hexagonal lattice subjected to a strong Rashba spin-orbit coupling (SOC). We focus on the marginal Abelian limit with the strength of SOC \ensuremathκ=\ensuremathπ/2\ensuremath{\kappa}=\ensuremath{\pi}/2\ensuremathκ=\ensuremathπ/2, where the derived Dirac fermions are spin-1/2 spinors in contrast to the pure hexagonal lattice. We find a double-degeneracy at the center of the Brillouin zone, which is a spin-3/2 Dirac-Weyl fermion that can be represented as two spin-1/2 fermions. While at the corner of the Brillouin zone, there occur another two spin-1/2 fermions. These Dirac spinors display a verity of spin textures beyond the usual topological properties. Furthermore, we investigate the energy spectrum of one-dimensional (1D) zigzag and armchair ribbons, and show that the appearance of a new cone at the center of the Brillouin zone can induce two flat bands in a 1D zigzag ribbon. These unique properties allow us to transport a single spin-1/2 Dirac spinor through the 1D zigzag ribbon with two quasi-two-dimensional leads, where only the spin-up or spin-down freedom of the Dirac spinors can transit through the ribbon.
We investigate the superfluidity of attractive Fermi gas in a square optical lattice with spin-orbit coupling (SOC). We show that the system displays a variety of new features. At half filling, SOC induces a Dirac semimetal and the system undergoes a semimetal-superfluid transition. Near half filling, we find that the superfluidity tends to be suppressed due to the emerging Dirac cones. While for small fillings, SOC can induce a BCS-BEC crossover beyond the conventional attractive Hubbard model, which is characterized by a bound state in the lattices. Moreover, we demonstrate that the superfluid density also exhibits many unusual properties in the lattices.
We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit-coupled attractive Fermi-Hubbard model can potentially be realized in cold-atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean-field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\mathrm{\ensuremath{\Gamma}}$ point, as found in earlier work. We identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a significantly improved maximum of about 10−−12.510--12.5%10−−12.5 of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field. Our work establishes a robust operating regime for experimenting with topological superfluids in cold-atom optical lattices.
We investigate the single-particle and collective excitations of a Rashba spin-orbit-coupled atomic Fermi gas with attractive interaction, loaded in a two-dimensional (2D) square optical lattice, in the presence of an effective out-of-plane Zeeman field. Our numerical calculations show that the many-body physics of the Bardeen-Cooper-Schrieffer (BCS) side is strongly modified compared to the Fermi gases in the free space. The physics behind this statement lies in the fact that in the 2D lattice case the single-particle ground-state energy is four times degenerated, while without a lattice structure the ground state is infinitely degenerate, and because of that, the spin-orbit coupling (SOC) in optical lattices gives rise to unusual properties entirely different from the continuum. For example, in the continuum, the pairing gap as well as the condensate fraction is strongly enhanced by the SOC strength on the BCS side. In the presence of lattice geometry the gap and the condensate fraction increase as a function of the SOC strength only at small fillings and a weak attraction limit. Moreover, we found that the speed of sound also exhibits different behavior: in the 3D and 2D continua, the slope of the Goldstone mode decreases as a function of the SOC strength, while in the lattice case the speed of sound increases monotonically with the SOC strength.
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.
We consider the quasi-one-dimensional (quasi-1D) system realized by an array of weakly coupled parallel one-dimensional ``tubes'' in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin-orbit coupling (SOC), and an sss-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T=0T=0T=0) Bogoliubov--de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the T=0T=0T=0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center-of-mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the three-dimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeeman-tuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.
The recent experimental realization of synthetic spin-orbit coupling (SOC) opens a new avenue for exploring novel quantum states with ultracold atoms. However, in experiments for generating two-dimensional SOC (e.g., Rashba type), a perpendicular Zeeman field, which opens a band gap at the Dirac point and induces many topological phenomena, is still lacking. Here, we theoretically propose and experimentally realize a simple scheme for generating two-dimensional SOC and a perpendicular Zeeman field simultaneously in ultracold Fermi gases by tuning the polarization of three Raman lasers that couple three hyperfine ground states of atoms. The resulting band gap opening at the Dirac point is probed using spin injection radio-frequency spectroscopy. Our observation may pave the way for exploring topological transport and topological superfluids with exotic Majorana and Weyl fermion excitations in ultracold atoms.