  The normal/superconducting phase boundary Tc has been calculated for
mesoscopic loops, as a function of an applied perpendicular magnetic field H.
While for thin-wire loops and filled disks the Tc(H) curves are well known, the
intermediate case, namely mesoscopic loops of finite wire width, have been
studied much less. The linearized first Ginzburg-Landau equation is solved with
the proper normal/vacuum boundary conditions both at the internal and at the
external loop radius. For thin-wire loops the Tc(H) oscillations are perfectly
periodic, and the Tc(H) background is parabolic (this is the usual Little-Parks
effect). For loops of thicker wire width, there is a crossover magnetic field
above which Tc(H) becomes quasi-linear, with the period identical to the Tc(H)
of a filled disk (i.e. pseudoperiodic oscillations). This dimensional
transition is similar to the 2D-3D transition for thin films in a parallel
field, where vortices start penetrating the material as soon as the film
thickness exceeds the temperature dependent coherence length by a factor 1.8.
For the presently studied loops, the crossover point is controlled by a similar
condition. In the high field '3D' regime, a giant vortex state establishes,
where only a surface superconducting sheath near the sample's outer radius is
present.
