Quantum phase transition in ultra small doubly connected superconducting cylinders

The kinetic energy of Cooper pairs, in doubly connected superconducting cylinders, is a function of the applied flux and the ratio between the diameter of the cylinder and the zero temperature coherence length d/ξ(0). If d >ξ(0) the known Little-Parks oscillations are observed. On the other hand if d <ξ(0), the superconducting state is energetically not favored around odd multiples of half flux quanta even at T∼0, resulting in the so called destructive regime [Y. Liu, et al., Science 294 (2001) 2332]. We developed a novel technique to fabricate superconducting doubly connected nanocylinders with both diameter and thickness less than 100 nm, and performed magnetoresistance measurements on such Nb and Al cylinders. In the Nb cylinders, where d >ξ(0), we observed the LP oscillations. In the Al cylinders we did not observe a transition to the superconducting state due to the proximity effect, resulted from an Au layer coating the Al. However, we did observe Altshuler-Aronov-Spivak (h/2e) oscillations in these cylinders