Noncontractible loop states from a partially flat band in a photonic borophene lattice

Abstract: Flat band systems are usually associated to compact localized states (CLSs) resulting from the macroscopic degeneracy of eigenstates at the flat band energy. In case of singular flat bands, these conventional localized flat band states have been found to be incomplete leading to the existence of so-called noncontractible loop states (NLSs) with nontrivial real space topology. Here, we experimentally and analytically demonstrate that a 2D photonic borophene lattice can host NLSs without a CLS counterpart because of a band that is flat only along high-symmetry lines and dispersive along others. We hence dispel the conventional wisdom that NLSs are necessarily linked to robust boundary modes due to a bulk-boundary correspondence. Originating from band touching protected by the band flatness, NLSs play a key role in studying the fundamental physics of flat band systems. Our results truly transform the current understanding of flat bands and could readily be transferred to a 2D material in the form of a planar sheet of boron atoms.