The superconductor-metal quantum phase transition in ultra-narrow wires

We present a complete description of a zero temperature phase transition between superconducting and diffusive metallic states in very thin wires due to a Cooper pair breaking mechanism originating from a number of possible sources. These include impurities localized to the surface of the wire, a magnetic field orientated parallel to the wire or, disorder in an unconventional superconductor. The order parameter describing pairing is strongly overdamped by its coupling to an effectively infinite bath of unpaired electrons imagined to reside in the transverse conduction channels of the wire. The dissipative critical theory thus 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 (equal to one in the physical case). The fluctuation corrections to the electrical and thermal conductivities are determined, and we find that the zero frequency electrical transport has a non-monotonic temperature dependence when moving from the quantum critical to low temperature metallic phase, which may be consistent with recent experimental results on ultra-narrow MoGe wires. Near criticality, the ratio of the thermal to electrical conductivity displays a linear temperature dependence and thus the Wiedemann-Franz law is obeyed. We compute the constant of proportionality in a systematic expansion and find a universal and experimentally verifiable fluctuation correction to the Lorenz number.;In the presence of quenched disorder, a novel algorithm is developed to solve the self-consistency condition arising when the number of complex order parameter components is taken to be large. In this limit, we find striking evidence for the flow to infinite randomness, and observe dynamically activated scaling consistent with predictions from the strong disorder renormalization group. Moreover, the infinite randomness fixed point of the pair-breaking superconductor-metal quantum phase transition is found to be in the same universality class as the onset of ferromagnetism in the one dimensional quantum Ising model in a random transverse field. This discovery may lead to the first calculations of real electrical transport in an experimentally relevant system exhibiting infinite randomness.