General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping

Abstract: 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, so we refer to them as general corner states. We analytically identify that the general corner states are induced by the intracelluar NNN hoppings (long-range interactions) and split off from the edge-state bands. Our work show a simple way to induce unique corner states by the long-range interactions, and offers opportunities for designing novel photonic devices.