Multiple boundary states in bilayer and decorated Su-Schrieffer-Heeger-like models

TL;DR

This paper explores multiple boundary states in extended SSH models, revealing coexistence and tunability of boundary states in bilayer and decorated configurations, advancing understanding of square-root topology.

Contribution

It introduces new extended SSH models supporting multiple boundary states, including those embedded in the bulk continuum, and elucidates their connection to square-root topology.

Findings

Coexistence of boundary states in bulk and band gaps.

Boundary states can be embedded into the bulk continuum.

Connection between decorated SSH-like models and their decomposed counterparts.

Abstract

Topological boundary states have attracted widespread fascination due to their series of intriguing properties. In this paper, we investigate the multiple boundary states within the two kinds of extended Su-Schrieffer-Heeger (SSH) models. The coexistence of boundary states that exist both in the bulk and band gaps is realized based on the bilayer SSH-like model, which consists of two conventional square-root SSH models that are directly coupled. We further show the square-root topology within the decorated SSH-like model, which supports multiple boundary states that could be embedded into the bulk continuum by tuning the hopping parameters. In addition, the connection between the decorated SSH-like model and its effectively decomposed counterparts is revealed. Our results broaden insight into the multiple boundary states and open up an exciting avenue for the future exploration of square-root topology.