  The kinetic energy of superconducting electrons in an ultrathin, doubly
connected superconducting cylinder, determined by the applied flux, increases
as the cylinder diameter decreases, leading to a destructive regime around
half-flux quanta and a superconductor to normal metal quantum phase transition
(QPT). Regular step-like features in resistance vs. temperature curves taken at
fixed flux values were observed near the QPT in ultrathin Al cylinders. It is
proposed that these features are most likely resulted from a phase separation
near the QPT in which normal regions nucleate in a homogeneous superconducting
cylinder.
