Topological edge states in curved zigzag superlattices in nonlinear exciton-polaritons

Zigzag chains allow for the formation of topological edge states. Several distinct chain architectures have been developed for this purpose. Here, we report a zigzag superlattice, containing two staggered sub-lattices, that supports multiple edge states, including higher-order modes. In such lattices, the intra- and intercell coupling is imbalanced by the tunneling effect of the eigenstates or deformation of the higher-order modes. We demonstrate that by arranging the zigzag superlattice into a curved shape, some of the edge states transition into bulk states as the curvature of the lattice increases, while some bulk states become more localized towards edge states. The reason is that a curved superlattice strengthens the intra-lattice coupling of the inner sub-lattice due to the separation reduction of the potential wells. %which, on the one hand, hinders the tunneling of the eigenstate to the outer sub-lattice and hence weakens the edge states formed in the inner sub-lattice. On the other hand, it can isolate more edge states formed in the outer sub-lattice, because of the induced more intensive deformation of the higher-order modes in the inner sub-lattice. We also show that some bulk states at larger curvatures can be transformed into edge states by a repulsive nonlinearity, which also enables the coexistence of different edge states. As a specific and ideal platform for realizing such topological superlattices we explore exciton-polaritons in semiconductor microcavities with their strong nonlinearity and possibility for optical excitation and control. Our work introduces an additional dimension for the design of complex topological lattices and functional photonic devices.