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

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