Realizing topological corner states in two-dimensional Su-Schrieffer-Heeger model with next-nearest neighbor couplings

Abstract

In the present work, we consider a two-dimensional Su-Schrieffer-Heeger model with alternating positive tunneling couplings between the neighboring sites. We show that introducing next-nearest neighbor couplings results in the emergence of topological corner states for some values of the corresponding tunneling coupling. Our work resolves the contradiction that arose when such corner states absent in the original two-dimensional Su-Schrieffer-Heeger model were observed experimentally in its photonic realization based on the array of cylindrical microwave resonators.

Characterization of the 2D Su–Schrieffer–Heeger Model with Second‐Nearest‐Neighbor Interactions

“…While in this work we study insulating materials, this illustrates the relevance of simple models to modeling real materials and forms a solid basis to build upon. Ivanova et al [ 20 ] use an electric circuit realization of a small 2D SSH grid to prove the existence of corner states in the SSH model with SNN interactions. In the work done by Xu et al [ 14 ] only intracellular interactions between the B and C sites are considered and studied numerically.…”