Edge states in trimer lattices

TL;DR

This paper investigates the topological edge states in a one-dimensional trimer lattice, revealing novel chiral edge modes that are robust to disorder and connecting them to topological invariants via a mapping to the Aubry-Andre9-Harper model.

Contribution

It introduces the existence of chiral edge states in inversion-symmetry broken phases of trimer lattices and links these states to topological properties through a mapping to the Aubry-Andre9-Harper model.

Findings

Chiral edge states can appear at a single edge in broken inversion symmetry phases.

Edge states are robust against large disorder.

Mapping to the Aubry-Andre9-Harper model reveals topological origins of edge modes.

Abstract

Topological phases of matter have attracted much attention over the years. Motivated by analogy with photonic lattices, here we examine the edge states of a one-dimensional trimer lattice in the phases with and without inversion symmetry protection. In contrast to the Su-Schrieffer-Heeger model, we show that the edge states in the inversion-symmetry broken phase of the trimer model turn out to be chiral, i.e., instead of appearing in pairs localized at opposite edges they can appear at a $\textit{single}$ edge. Interestingly, these chiral edge states remain robust to large amounts of disorder. In addition, we use the Zak phase to characterize the emergence of degenerate edge states in the inversion-symmetric phase of the trimer model. Furthermore, we capture the essentials of the whole family of trimers through a mapping onto the commensurate off-diagonal Aubry-Andr\'e-Harper model, which allow us to establish a direct connection between chiral edge modes in the two models, including the calculation of Chern numbers. We thus suggest that the chiral edge modes of the trimer lattice have a topological origin inherited from this effective mapping. Also, we find a nontrivial connection between the topological phase transition point in the trimer lattice and the one in its associated two-dimensional parent system, in agreement with results in the context of Thouless pumping in photonic lattices.