$\mathbb{Z}_2$ topological insulator analog for vortices in an interacting bosonic quantum fluid

TL;DR

This paper demonstrates a topologically protected vortex propagation in an interacting bosonic quantum fluid, creating an analog of a $ ext{Z}_2$ topological insulator for quantum vortices, overcoming limitations of non-interacting systems.

Contribution

It introduces a novel topological protection mechanism for vortices in a Bose-Einstein Condensate using valley winding coupling, enabling true topological insulator behavior for bosonic excitations.

Findings

Vortex winding number couples with valley degree of freedom.

Chiral vortex propagation is protected against backscattering.

The system acts as a $ ext{Z}_2$ topological insulator for vortices.

Abstract

$\mathbb{Z}_2$ topological insulators for photons and in general bosons cannot be strictly implemented because of the lack of symmetry-protected pseudospins. We show that the required protection can be provided by the real-space topological excitation of an interacting quantum fluid: quantum vortex. We consider a Bose-Einstein Condensate at the $\Gamma$ point of the Brillouin zone of a quantum valley Hall system based on two staggered honeycomb lattices. We demonstrate the existence of a coupling between the winding number of a vortex and the valley of the bulk Bloch band. This leads to chiral vortex propagation at the zigzag interface between two regions of inverted staggering, where the winding-valley coupling provides true topological protection against backscattering, contrary to the interface states of the non-interacting Hamiltonian. This configuration is an analog of a $\mathbb{Z}_2$ topological insulator for quantum vortices.