Orbital Edge and Corner States in Su-Schrieffer-Heeger Optical Lattices

In the past decade, topological photonics has proved to be one of the most active research fields with interdisciplinary interest [1] . In particular, the Su-Schrieffer-Heeger (SSH) model [2] , [3] representing a prototypical one-dimensional (1D) topological system has received a great amount of attention due to the simplicity of its energy band structure exhibiting nontrivial chiral topological modes. In its basic 1D version, the two-level bandgap depends on the absolute difference between intra- and inter-cell coupling, singling out the band topology associated with the Zak phase [2] . Two-dimensional (2D) SSH configurations can typically support zero-dimensional corner states regardless of their physical dimensions, making it a useful candidate as a testbench for understanding high-order topological insulators (HOTIs) [4] – [7] . Thus far, most endeavors with such SSH systems have been focused on the fundamental topological states. Here, we report high-order topological states in finite SSH photonic lattices, with emphasis on orbital (or p-) states in both 1D and 2D systems. Interest arises from the fact that such modes present robust and stable proprieties [8] – [9] .