Boundary-induced topological transition in an open SSH model

TL;DR

This paper investigates how attaching leads to an open SSH chain influences its topological properties, revealing a transition from topological to trivial phases and the emergence of phase-inverted edge states due to coupling effects.

Contribution

It introduces an effective Hamiltonian approach to analyze the open SSH model, uncovering the emergence of phase-inverted edge states and the impact of lead coupling on topological phases.

Findings

Hybridization of edge states with increased coupling

Emergence of phase-inverted edge states in the trivial phase

Identification of three regimes of topological behavior

Abstract

We consider a Su-Schrieffer-Heeger chain to which we attach a semi-infinite undimerized chain (lead) to both ends. We study the effect of the openness of the SSH model on its properties. A representation of the infinite system using an effective Hamiltonian allows us to examine its low-energy states in more detail. We show that, as one would expect, the topological edge states hybridize as the coupling between the systems is increased. As this coupling grows, these states are suppressed, while a new type of edge state emerges from the trivial topological phase. These new states, referred to as phase-inverted edge states, are localized low-energy modes very similar to the edge states of the topological phase. Interestingly, localization occurs on a new shifted interface, moving from the first (and last) site to the second (and second to last) site. This suggests that the topology of the system is strongly affected by the leads, with three regimes of behavior. For very small coupling the system is in a well-defined topological phase; for very large coupling it is in the opposite phase; in the intermediate region, the system is in a transition regime.