Surface waves and bulk Ruderman mode of a bosonic superfluid vortex crystal in the lowest Landau level

TL;DR

This paper investigates collective excitations in a finite vortex crystal within a bosonic superfluid under artificial magnetic fields, revealing chiral surface waves and a Ruderman bulk mode through microscopic and effective field theory analyses.

Contribution

It introduces a detailed analysis of surface and bulk modes in a vortex crystal using Gross-Pitaevskii and Bogoliubov-de Gennes equations, including the identification of a Ruderman mode.

Findings

Discovery of chiral surface waves with frequencies above bulk modes

Identification of a low-frequency Ruderman bulk mode

Validation of the Ruderman mode with effective field theory

Abstract

We determine and analyze collective normal modes of a finite disk-shaped two-dimensional vortex crystal formed in a compressible bosonic superfluid in an artificial magnetic field. Using the microscopic Gross-Pitaevskii theory in the lowest Landau level approximation, we generate vortex crystal ground states and solve the Bogoliubov-de Gennes equations for small amplitude collective oscillations. We find chiral surface waves that propagate at frequencies larger than those of the bulk Tkachenko modes. Furthermore, we study low frequency bulk excitations and identify a torsional Ruderman mode, which we find is well-described by a previously developed low-energy effective field theory.