Menz Philip, Hanafi Haissam, Imbrock Jörg, Denz Cornelia
Institute of Applied Physics, University of Münster, Münster, Germany.
Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany.
Nanophotonics. 2023 Jul 31;12(17):3409-3415. doi: 10.1515/nanoph-2023-0222. eCollection 2023 Aug.
Flat band systems are commonly associated with compact localized states (CLSs) that arise from the macroscopic degeneracy of eigenstates at the flat band energy. However, in the case of singular flat bands, conventional localized flat band states are incomplete, leading to the existence of noncontractible loop states (NLSs) with nontrivial real-space topology. In this study, we experimentally and analytically demonstrate the existence of NLSs in a 2D photonic borophene lattice without a CLS counterpart, owing to a band that is flat only along high-symmetry lines and dispersive along others. Our findings challenge the conventional notion that NLSs are necessarily linked to robust boundary modes due to a bulk-boundary correspondence. Protected by the band flatness that originates from band touching, NLSs play a significant role in investigating the fundamental physics of flat band systems.
平带系统通常与紧凑局域态（CLSs）相关联，这些紧凑局域态源于平带能量处本征态的宏观简并。然而，在奇异平带的情况下，传统的局域平带态是不完整的，导致存在具有非平凡实空间拓扑结构的不可收缩环态（NLSs）。在本研究中，我们通过实验和分析证明了在二维光子硼烯晶格中存在没有CLS对应物的NLSs，这是由于存在一个仅沿高对称线平坦而沿其他方向色散的能带。我们的发现挑战了传统观念，即由于体-边界对应关系，NLSs必然与稳健的边界模式相关联。受源于能带接触的能带平坦性保护，NLSs在研究平带系统的基本物理方面发挥着重要作用。
