Coexistence of vortex arrays and surface capillary waves in spinning prolate superfluid He-4 nanodroplets

TL;DR

This study uses Density Functional Theory to explore how vortex arrays and surface capillary waves coexist in spinning superfluid helium-4 nanodroplets, revealing size-dependent vortex presence and complex rotational behavior.

Contribution

It provides the first detailed analysis of vortex and capillary wave coexistence in prolate superfluid helium droplets, highlighting size effects and deviations from classical rotation models.

Findings

Small droplets are vortex-free at equilibrium.

Vortex arrays coexist with capillary waves in large droplets.

Rotational properties depend on droplet size and vortex count.

Abstract

Within Density Functional Theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate He-4 droplets made of several thousands of helium atoms. Surface capillary waves are ubiquitous in prolate superfluid He-4 droplets and, depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex-free, evolving towards vortex-hosting as the droplet size increases. This result is in agreement with a recent experiment [S.M. O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)], where it has been disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. Contrarily to viscous droplets executing rigid body rotation, the stability phase diagram of spinning He-4 droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host.