Theory of the pairbreaking superconductor-metal transition in nanowires

TL;DR

This paper develops a theoretical framework for the superconductor-metal transition in thin nanowires caused by pair-breaking, analyzing fluctuations, phase diagrams, and transport properties with potential experimental relevance.

Contribution

It introduces a comprehensive critical theory for the superconductor-metal transition in nanowires, including fluctuation effects and transport predictions, extending understanding of quantum phase transitions in low-dimensional systems.

Findings

Electrical conductivity shows non-monotonic temperature dependence.

Thermal to electrical conductivity ratio is linear in temperature.

Wiedemann-Franz law holds with a universal Lorenz number.

Abstract

We present a detailed description of a zero temperature phase transition between superconducting and diffusive metallic states in very thin wires due to a Cooper pair breaking mechanism. The dissipative critical theory contains current reducing fluctuations in the guise of both quantum and thermally activated phase slips. A full cross-over phase diagram is computed via an expansion in the inverse number of complex components of the superconducting order parameter (one in the physical case). The fluctuation corrections to the direct current electrical and thermal conductivities are determined, and we find that the electrical conductivity has a non-monotonic temperature dependence in the metallic phase which may be consistent with recent experimental results on ultra-narrow wires. In the quantum critical regime, the ratio of the thermal to electrical conductivity displays a linear temperature dependence and thus the Wiedemann-Franz law is obeyed, with a new universal experimentally verifiable Lorenz number.