Emerging topological bound states in Haldane model zigzag nanoribbons

TL;DR

This paper investigates topological bound states in Haldane model zigzag nanoribbons, revealing robust in-gap states at the edges that are sensitive to ribbon width and supported by Zak phase analysis.

Contribution

It introduces the emergence of reentrant topological phases with in-gap bound states in Haldane nanoribbons, highlighting their robustness and dependence on ribbon width.

Findings

Bound states are localized at the ends of the nanoribbons.

These states are robust against on-site disorder.

Topological properties are sensitive to the strip width.

Abstract

Zigzag nanoribbons hosting the Haldane Chern insulator model are considered. In this context, a reentrant topological phase, characterized by the emergence of quasi zero dimensional in-gap states, is discussed. The bound states, which reside in the gap opened by the hybridization of the counter-propagating edge modes of the Haldane phase, are localized at the ends of the strip and are found to be robust against on-site disorder. These findings are supported by the behavior of the Zak phase over the parameter space, which exhibits jumps of $\pi$ in correspondence to the phase transitions between the trivial and the non-trivial phases. The effective mass inversion leading to the jumps in the Zak phase is interpreted in a low energy framework. Setups with non-uniform parameters also show topological bound states via the Jackiw-Rebbi mechanism. All the properties reported are shown to be extremely sensitive to the strip width.