Session Y1: Superconductivity and Quantum Transport in Nanowires

Mapping out the Superconductor-Insulator Phase Diagram for Nanowires.

We establish the superconductor-insulator phase diagram for quasi-one-dimensional wires by measuring about 100 MoGe nanowires with length in a range 30-500 nm. All wires can be clearly separated into two groups: superconducting ones with the wire resistance dropping rapidly with cooling, roughly following the Arrhenius activation law, and insulating wires, which exhibit a weak Coulomb blockade behavior. The phase boundary between superconducting and insulating wires is consistent with the Chakravarty-Schmid-Bulgadaev criteria, namely with the critical resistance of a wire being equal to quantum resistance, i.e. 6.5 kOhms. We argue that small deviations from this phase boundary in short thin wires are caused by magnetic moments that forms on a wire surface. The evidence for the presence of the moments comes from an anomalous enhancement of the critical current by magnetic field detected at low temperatures.   

Statistics of superconductive-resistive switching in nanowires: An effective probe for resolving phase-slip events

Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states and impart a non-zero resistance to superconducting nanowires. They play a fundamental role in determining the fate of superconductivity in nanowires. Conversely, superconducting nanowires provide an ideal setting for accessing non-trivial fluctuations driven by thermal activation and---at low temperatures---by quantum tunneling of a one-dimensional field. However, this potential has not been fully realized because resistance measurements, on the one hand, are capable of capturing only the averaged phase-slip behavior, and on the other hand, are incapable of pinning down the low temperature phase-slip behavior, as the measured resistance values drop below the noise floor. On going beyond the linear-response regime, the I-V characteristics show a hysteretic behavior. As the current is ramped up repeatedly, the state switches from a superconductive to a resistive one, doing so at somewhat random current values below the depairing critical current. The distribution of these switching currents was studied recently [1]. In this talk, I will report on the rather counter-intuitive temperature dependence of the distribution and its theoretical understanding via a stochastic model developed in Ref [2]. I will show that although, in general, several phase-slip events are necessary to induce switching, there is an experimentally accessible temperature- and current-range for which a single phase-slip event is sufficient to switch the wire to the normal (resistive) state. I will conclude by arguing that switching-current statistics provide an effective probe to resolve individual phase-slip events and in addition offer unprecedented access to quantum phase-slip tunneling events. \\[4pt] [1] M. Sahu, M.-H. Bae, A. Rogachev, D. Pekker, T.-C. Wei, N. Shah, P. M. Goldbart, and A. Bezryadin, arXiv:0804.2251\\[0pt] [2] N. Shah, D. Pekker, and P. M. Goldbart, Phys. Rev. Lett. 101, 207001 (2008)   

Theory of the pairbreaking superconductor-metal transition in nanowires

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 electrical ($\sigma$) and thermal ($\kappa$) conductivities are determined, and we find that $\sigma$ 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. We also examined the influence of quenched disorder on the superconductor-metal transition. The self-consistent pairing eigenmodes of a quasi-one dimensional wire were determined numerically. Our results support the proposal by Hoyos {\em et al.\/} (Phys. Rev. Lett. {\bf 99}, 230601 (2007)) that the transition is described by the same strong disorder fixed point describing the onset of ferromagnetism in the quantum Ising model in a transverse field.   

Thermally activated phase slips in superconducting nanowires

We reanalyze the problem of thermally activated phase slips which can dominate the behavior of sufficiently thin superconducting wires at temperatures close to T$_c$. With the aid of an effective action approach we evaluate the TAPS rate which turns out to exceed the rate found by McCumber and Halperin, Phys. Rev. B 1, 1054 (1970) within the time-dependent Ginzburg-Landau analysis by the factor 1/(1-T/TC). Additional differences in the results of these two approaches arise at bias currents close to the Ginzburg-Landau critical current where the TAPS rate becomes bigger. We also derive a simple formula for the voltage noise across the superconducting wire in terms of the TAPS rate. Our results can be verified in modern experiments with superconducting nanowires.