Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of the isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small fields the $L$=0 state qualitatively behave like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As field is increased the discontinuity changes to a smooth change which is a finite size effect. Hence this may give us insight into a continuous crossover from bulk like to mesoscopic behavior. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to paramagnetic Meissner effect and can lead to unambiguous observation of positive magnetization in mesoscopic superconductors.