Edge states and topological insulating phases generated by curving a nanowire with Rashba spin-orbit coupling

TL;DR

This paper demonstrates that periodic curvature in nanowires with Rashba spin-orbit coupling can induce topological insulating phases with protected edge states, revealing a link between geometry and topology in nanomaterials.

Contribution

It shows how curvature effects can generate topological phases and edge states in nanowires, a novel mechanism for topological matter.

Findings

Curvature induces insulating phases with butterfly spectra.

Localized topologically protected end states appear in gaps.

Certain periods lead to topologically non-trivial phases at half-filling.

Abstract

We prove that curvature effects in low-dimensional nanomaterials can promote the generation of topological states of matter by considering the paradigmatic example of quantum wires with Rashba spin-orbit coupling, which are periodically corrugated at the nanometer scale. The effect of the periodic curvature generally results in the appearance of insulating phases with a corresponding novel butterfly spectrum characterized by the formation of fine measure complex regions of forbidden energies. When the Fermi energy lies in the gaps, the system displays localized end states protected by topology. We further show that for certain corrugation periods the system possesses topologically non-trivial insulating phases at half-filling. Our results suggest that the local curvature and the topology of the electronic states are inextricably intertwined in geometrically deformed nanomaterials.