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

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.