Duality picture of Superconductor-insulator transitions on Superconducting nanowire

In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature T-c was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory.