  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.
