Theoretical seminar | 06 October 2021
Higher-order topological insulating phases (HOTIs) have attracted much attention in photonics due to their extreme localization and robustness to disorder. On the other hand, orbital hybridization in photonic systems could induce exotic band structures such as Dirac cones and flat bands , and also implicitly leads to nontrivial higher-order topology in the shrunken-expanded honeycomb  and Kagome lattices, where the degeneracy of several metaatom orbital modes is protected by the lattice symmetry. Here, with intuition gained from a recent 1D realization , we find two waveguide models where accidental orbital degeneracy leads to the higher-order topology, while the single-orbital limit is trivial or of lower topological order. First, we show that s-f hybridized waveguide kagome lattice is a multipolar HOTI which is not topologically equivalent to any known HOTI class. This model hosts midgap corner states as well as detached edge states. For fine-tuned mode coupling constants, all bands become flat, which enables complete photonic caging without any effective magnetic fields . Second, we find an unconventional HOTI phase in s-d hybridized waveguide square lattice with Su-Schrieffer-Heeger (SSH) alternating structure of couplings. This model reduces to two anisotropic 2D SSH layers , each for a single orbital pseudospin, and both in their HOTI phases. Our work paves a way towards higher-order topology which is protected by crystalline symmetries only partially, while some protection is provided by the symmetries of accidental on-site orbital degeneracies.
Main paper/arXiv, related to the seminar, and other references
 X. Huang, Y. Lai, Z. Hang et al., Nature Mater. 10, 582–586 (2011).  L.-H. Wu and X. Hu, Phys. Rev. Lett. 114, 223901 (2015).  R. S. Savelev and M. A. Gorlach, Phys. Rev. B 102, 161112 (2020).  J. Vidal, R. Mosseri, and B. Douçot, Phys. Rev. Lett. 81, 5888 (1998).  B.-Y. Xie et al., Phys. Rev. B 98, 205147 (2018).