Fig. 5: Example of extension to a large lattice: Union Jack lattice.
From: Programmable synthetic magnetism and chiral edge states in nano-optomechanical quantum Hall networks
a Square tiling of the W5 network forms a Union Jack (UJ) lattice, featuring a two-site primitive unit cell (gray). b Two-dimensional band structure of a Union Jack lattice pierced by flux Φ = π/2. Two bands with opposite Chern numbers C = ± 1 are identified, separated by a gap. c Band structure of a UJ ribbon, finite in the x-direction (width N = 33 sites) and infinite in y. Two edge states traverse the topological gap, localized on either boundary of the ribbon. d Transverse edge state profiles in a unit cell of the UJ ribbon, at different values of ky indicated by the colored dots in panel c. The panels show a single unit cell of the ribbon, which is extended to the top and bottom. The states are localized at one edge of the ribbon, depending on propagation direction. The transverse decay length depends on ky. For ky = ± π/2, edge states fully localize on the outer two sites.
