Robust flat bands of the honeycomb wire network

TL;DR

This paper demonstrates that honeycomb wire networks naturally host robust, exact flat bands across the entire Brillouin zone, driven by symmetry and lattice structure, with potential applications in electronic systems.

Contribution

It reveals the universal presence of flat bands in honeycomb wire networks, independent of microscopic details, and shows their robustness in realistic experimental setups.

Findings

Flat bands span the entire Brillouin zone in honeycomb networks.

Flat bands are robust against microscopic variations and persist in realistic systems.

Existence of compact localized states satisfying a Bohr-Sommerfeld quantization.

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.