Elastic modes of vortex configurations in thin disks

Within the London limit, we investigate the dynamics of stable vortex configurations in small thin superconducting disks by studying their elastic modes. The elastic modes are a mixture of shearlike and compressionlike modes. More pronounced shearlike behavior is found for the low-energy eigenmodes, while a compressionlike content is more prominent for higher eigenmodes. The eigenmode associated with a pure rotation of the entire system is always zero. Highly symmetric stable configurations - in which the number of vortices in different shells are multiples of each other - have several degenerate modes, in contrast with nonsymmetric configurations, which have a less degenerate spectrum. The second lowest-energy mode is nearly zero in configurations of the latter type, while is clearly nonzero for highly symmetric configurations. This suggests that symmetric configurations are more stable against fluctuations, which is important in the development of new superconducting devices. The present work could also be applied to electric charges confined within a cylindrical hole inside a metal and submitted to a parabolic electric potential.