Dissipation-driven phase transitions in superconducting wires

Narrow superconducting wires with diameter $d\ll\xi_{0}$ (where $\xi_{0}$ is the bulk superconducting coherence length) are quasi-1D systems in which fluctuations of the order parameter strongly affect low-temperature properties. Indeed, fluctuations cause the magnitude of the order parameter to temporarily vanish at some point along the wire, allowing its phase to slip by $2\pi$, and to produce finite resistivity for all temperatures below $T_c$. In this work, we show that a weak coupling to a diffusive metallic film reinforces superconductivity in the wire through a quench of phase fluctuations. 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 towards a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. Finally we discuss implications for the DC resistivity of the wire.