Superconductor-to-normal transitions in dissipative chains of mesoscopic grains and nanowires

Abstract

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed and the results are applied to nanowires. It is shown that in one dimensional arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase (FSC), each grain acts superconducting, and the coupling to the dissipative conduction is important. In the ${\mathrm{SC}}^{\star }$ phase, the dissipation is irrelevant at long wavelengths. The transition between these two phases is driven by quantum phase slip dipoles, and is primarily local, with continuously varying critical exponents. In contrast, the transition from the ${\mathrm{SC}}^{\star }$ phase to the normal metallic phase is a Kosterlitz-Thouless transition with global character (i.e., determined by the field behavior at large wavelengths). Most interesting is the transition from the FSC phase directly to the normal phase: this transition, which has mixed local and global characteristics, can be one of three distinct types. The corresponding segments of the phase boundary come together at bicritical points. The zero-temperature phase diagram, as well as the finite-temperature scaling behavior are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.