Dear Soma,

Your question is not completely clear to me. I can think of the following two situations:

1) The quantum dot is not made of superconducting material, but is surrounded or in contact with a superconductor. In that case superconducting electrons may flow through the quantum dot, as if the quantum dot itself is superconducting.

2) the quantum dot is made out of superconductor. In that case the quantum dot could be superconducting if it is large enough, i.e. large compared to the superconducting coherence length. For a thin wire that has two dimensions smaller than the coherence length, so called phase slips can occur in the material and the wire loses its superconducting properties. Similarly, a very narrow constriction acts as a weak link or Josephson junction where the phase may jump. Based on this experience with wires I would be tempted to say that quantum dots that are smaller than th coherence length in all 3 dimensions do not show superconductivity in a way that is similar to the bulk phenomenon.

Dear Soma,

Your question is not completely clear to me. I can think of the following two situations:

1) The quantum dot is not made of superconducting material, but is surrounded or in contact with a superconductor. In that case superconducting electrons may flow through the quantum dot, as if the quantum dot itself is superconducting.

2) the quantum dot is made out of superconductor. In that case the quantum dot could be superconducting if it is large enough, i.e. large compared to the superconducting coherence length. For a thin wire that has two dimensions smaller than the coherence length, so called phase slips can occur in the material and the wire loses its superconducting properties. Similarly, a very narrow constriction acts as a weak link or Josephson junction where the phase may jump. Based on this experience with wires I would be tempted to say that quantum dots that are smaller than th coherence length in all 3 dimensions do not show superconductivity in a way that is similar to the bulk phenomenon.

I completely agree with Food.

Dear Soma and Dood,

                                   Once all the characteristic lengths are larger than your nanostructure size one can expect that, as the scattering process is suppressed. But superconductivity requires some persistent current flow through the nanostructure. So i suggest "Quantum Rings"- a complete nanostructure, for your present interest. 

"Persistent Current Inherently Present Here".