General bounded corner states in the two-dimensional Su-Schrieffer-Heeger model with intracellular next-nearest-neighbor hopping

We investigate corner states in a photonic two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model on a square lattice with zero gauge flux. By considering intracelluar next-nearest-neighbor (NNN) hoppings, we discover a broad class of corner states in the 2D SSH model and show that they are robust against certain fabrication disorders. Moreover, these corner states are located around the corners but not at the corner points. We analytically identify that these corner states are induced by the intracelluar NNN hoppings (long-range interactions) and split off from the edge-state bands. Thus, we refer to them as general bounded corner states. Our paper shows a simple way to induce unique corner states by the long-range interactions and offers opportunities for designing novel photonic devices.