  In high-quality nanowires, quantum confinement of the transverse electron
motion splits the band of single-electron states in a series of subbands. This
changes in a qualitative way the scenario of the magnetic-field induced
superconductor-to-normal transition. We numerically solve the Bogoliubov-de
Gennes equations for a clean metallic cylindrical nanowire at zero temperature
in a parallel magnetic field and find that for diameters D < 10-15 nm, this
transition occurs as a cascade of subsequent jumps in the order parameter (this
is opposed to the smooth second-order phase transition in the mesoscopic
regime). Each jump is associated with the depairing of electrons in one of the
single-electron subbands. As a set of subbands contribute to the order
parameter, the depairing process occurs as a cascade of jumps. We find
pronounced quantum-size oscillations of the critical magnetic field with giant
resonant enhancements. In addition to these orbital effects, the paramagnetic
breakdown of Cooper pairing also contributes but only for smaller diameters, i.
e., D < 5 nm.
