Extensions to the Su-Schrieffer-Heeger model: Ribbons and their topological properties

Abstract

The Su-Schrieffer-Heeger (SSH) model describes the hopping of spinless fermions in a one-dimensional bipartite lattice with staggered hopping potentials. We extend, by modifying the geometry of the chains, the SSH model into two types, which we call the Type 1 and the Type 2 extensions. The Type 1 extension is a linear chain of diamonds while the Type 2 extension is a linear hexagonal chain. We use exact diagonalization to determine the energy spectrum and corresponding eigenstates of the particles in the chain. We find that the Type 1 extension shows the appearance of a flat energy band in the bulk and edge states when the chain is finite. Edge states also appear in the Type 2 extension.