Dissipation-driven phase transitions in superconducting wires

We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization group and a self-consistent variational approach to obtain the critical points and phases at $T=0$. We predict a quantum phase transition toward a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the dc resistivity of the wire.

Figure 1

(Color online) Representation of the system. At $T⪡T_c$ one-particle hopping is suppressed by the BCS gap-energy ${\Delta }_0$. At next order in the hopping process, Cooper pairs can tunnel into the metal and propagate coherently in a length ${\xi }_N$, generating an effective coupling $\sim \text{cos}\left[\theta \left(\mathit{r}\right)-\theta \left({\mathit{r}}^{\prime }\right)\right]$ in the wire.

Figure 2

(Color online) Normalized resistivity vs $T/T_0$. As the (dimensionless) Andreev conductance ${\tilde{G}}_A$ is increased, the wire resistivity $\varrho$ $\left(T\right)$ deviates from the law $\sim T^{2K-3}$ predicted for an isolated wire (Refs. 29, 30, 33) as a consequence of the dissipation-induced increase in the stiffness $K$ [cf. Eq. (15)].