Zero-energy Edge States of Tight-Binding Models for Generalized Honeycomb-Structured Materials

Generalized honeycomb-structured materials have received increasing attention due to their novel topological properties. In this article, we investigate zero-energy edge states in tight-binding models for such materials with two different interface configurations: type-I and type-II, which are analog to zigzag and armchair interfaces for the honeycomb structure. We obtain the necessary and sufficient conditions for the existence of such edge states and rigorously prove the existence of spin-like zero-energy edge states. More specifically, type-II interfaces support two zero-energy states exclusively between topologically distinct materials. For type-I interfaces, zero-energy edge states exist between both topologically distinct and identical materials when hopping coefficients satisfy specific constraints. We further prove that the two energy curves for edge states exhibit strict crossing. We numerically simulate the dynamics of edge state wave packets along bending interfaces, which agree with the topologically protected motion of spin-like edge states in physics.