p-Orbital Higher-Order Topological Corner States in 2D Photonic Su–Schrieffer–Heeger Lattices

Higher-order topological insulators (HOTIs) have attracted much attention in photonics partly because of the robust and highly confined corner modes they support. The growing availability of synthetic multi-orbital platforms has recently stimulated research focus on the interplay between HOTIs and orbital degree of freedom. In this work, the topological properties of the two-dimensional (2D) Su–Schrieffer–Heeger (SSH) model with $p$-orbital degree of freedom are explored and $p$-orbital topological corner states in a laser-written photonic 2D SSH lattice are experimentally observed. It is shown that the $p$-band 2D SSH model is a HOTI, where zero-energy orbital corner states appear either as in-gap states or as bound states in the continuum (BICs). Chiral symmetry is sufficient for topological protection of the in-gap $p$-orbital corner states, but not for their BIC counterparts because of the hybridization effect within the bulk continuum. The multipole chiral number is employed as an optimal topological invariant to characterize the $p$-orbital HOTIs. The flexibility of tuning the orbital couplings offers an extra degree of manipulation for the BICs, which may be useful for the development of novel photonic devices.