Resistance induced by quantum phase-slips in superconducting nanowires

We have measured the resistive transitions of ∼20 nanowires of superconducting amorphous MoGe with diameters View the MathML source and lengths from 100 to View the MathML source. The transition width increases with decreasing cross-sectional area (i.e. increasing normal resistance per unit length) as described by the phenomenology including quantum phase-slips used by Giordano to explain his earlier data and also by the rather similar results of a microscopic theory of Golubev and Zaikin. The resistance well below Tc is much greater than can be explained by thermally activated phase-slips alone. We consider this to strongly support the reality of quantum phase-slips, and the basic correctness of these theories. The exact role of dissipation, whether from metal in the wire, from the carbon nanotube substrate, or from the electromagnetic environment, in reducing quantum phase-slips needs further clarification.