Vortex dynamics and persistent current decay in thin superfluidHe4films

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Abstract
A systematic analysis of vortex dynamics based on the Kosterlitz-Thouless theory for two-dimensional phase transitions is carried out to study theoretically the decay of persistent current in thin superfluid helium films. The relaxation of vortex density due to both bulk and edge processes is considered in parallel with the dissipation of persistent current. The relaxation effects are shown to be important for thin films where bulk processes dominate, but not for thick films with prevailing wall processes. The pinning-center effects are studied within a phenomenological model and turn out to play an essential role for films of intermediate thickness at the late stage of current decay. The screening due to free vortices is discussed self-consistently in the Debye-Hückel approximation and is shown to be substantial in the onset region. The theoretical results are compared quantitatively with the experimental data of Ekholm and Hallock [Phys. Rev. B 21, 3902 (1980)] on persistent current decay. The memory effect observed in experiment is interpreted as a consequence of the vortex density relaxation.