Figure 2: The spin-dependent hexagonal lattice.
From: Chiral magnetism and spontaneous spin Hall effect of interacting Bose superfluids

(a) The lattice structure. Spin ↑ (↓) bosons mainly live on A (B) sites. (b) The condensate configuration for the chiral spin superfluid. Spin ↑ and ↓ condensing at +K and −K in the first excited band corresponds to spin loop currents in real space, as illustrated by dashed arrows in a. (c) A contour plot of the excited band Wannier function of spin ↑, which is peaked at the A sites and has a minimum at the B sites (the opposite is true for the spin ↓ Wannier function).