Thermally Assisted Penetration and Exclusion of Single Vortex in   Mesoscopic Superconductors
  A single vortex overcoming the surface barrier in a mesoscopic superconductor with lateral dimensions of several coherence lengths and thickness of several nanometers provides an ideal platform to study thermal activation of a single vortex. In the presence of thermal fluctuations, there is non-zero probability for vortex penetration into or exclusion from the superconductor even when the surface barrier does not vanish. We consider the thermal activation of a single vortex in a mesoscopic superconducting disk of circular shape. To obtain statistics for the penetration and exclusion magnetic fields, slow and periodic magnetic fields are applied to the superconductor. We calculate the distribution of the penetration and exclusion fields from the thermal activation rate. This distribution can also be measured experimentally, which allows for a quantitative comparison. 
Shi-Zeng Lin, Takahiro Nishio, Lev N. Bulaevskii, Matthias J. Graf and   Yukio Hasegawa
cond-mat.supr-con cond-mat.stat-mech