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

TL;DR

This paper demonstrates that a 2D photonic borophene lattice hosts noncontractible loop states (NLSs) without conventional localized states, challenging existing notions about flat band topologies and expanding understanding of flat band physics.

Contribution

It reveals the existence of NLSs in a partially flat band system without associated compact localized states, providing new insights into flat band topologies.

Findings

NLSs can exist without CLS counterparts in a 2D photonic lattice.

Flat bands along high-symmetry lines can host nontrivial topological states.

Results challenge the conventional bulk-boundary correspondence in flat band systems.

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.