Tunneling spectroscopy of giant vorticity states in superconducting micro- and nanorings at ultra-low temperatures

When a superconducting contour is exposed to a magnetic field screening currents are induced. At temperatures well below the critical temperature T_c periodicity of the persistent currents can significantly exceed the superconducting flux quantum h/2e due to formation of metastable energy states with high quantum winding numbers (vorticity). We have studied the effect in normal metal-insulator-superconductor (NIS) and SIS'IS tunnel structures with the superconducting (S or S') electrode in a shape of a loop. The tunnel current oscillates due to the modulation of the superconducting density of states by the persistent currents reaching the sub-critical values. In the limit of loops with extremely narrow linewidth the magnitude of the oscillations drops and their shape deviates from the 'conventional' saw-tooth behavior. The effect can be accounted to the contribution of the quantum phase slips in the ultra-narrow superconducting ring-shaped electrode