Robust flat bands of the honeycomb wire network

Abstract: We show that periodic honeycomb networks of ballistic conducting channels generically host exact flat bands spanning the entire Brillouin zone. These flat bands are independent of microscopic vertex scattering, persist for any number of transverse modes, and occur in a universal $1\colon 2$ ratio with dispersive bands. Their existence is enforced by local $D_3$ vertex symmetry and lattice translations. We construct compact localized states obeying a Bohr-Sommerfeld-type quantization condition and demonstrate that flat bands survive in realistic antidot lattices, establishing honeycomb wire networks as a robust flat band platform relevant to gated high-mobility 2D electron gases and molecule-patterned metallic surfaces.