Robust zero-energy bound states in a helical lattice

TL;DR

This paper investigates a one-dimensional helical lattice model revealing a topologically nontrivial phase that supports zero-energy boundary modes, which are robust and always embedded within the continuum band, with implications for surface states in certain materials.

Contribution

It introduces a topological invariant for a helical lattice model and establishes strict conditions for zero-energy boundary modes, expanding understanding of topological phases in atomic-scale helices.

Findings

Identifies a topological phase supporting zero-energy boundary modes.

Derives a topological invariant related to zero-energy end modes.

Discusses practical implications for surface states in specific materials.

Abstract

Atomic-scale helices exist as motifs for several material lattices. We examine a tight-binding model for a single one-dimensional monatomic chain with a p-orbital basis coiled into a helix. A topologically nontrivial phase emerging from this model supports a zero-energy mode localized to a boundary, always embedded within a continuum band, regardless of termination site. We identify a topological invariant for this phase that is related to the number of zero energy end modes by means of the bulk-boundary correspondence, and give strict conditions for the existence of the bound state. Another, non-topological, gapped edge mode in the model spectrum has practical consequences for surface states in e.g. trigonal tellurium and selenium and other van der Waals-bonded one-dimensional semiconductors.