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Pekker, D., Shah, N., Sahu, M., Bezryadin, A., & Goldbart, P. M. (2009). Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires. Phys. Rev. B, 80, 214525 (1 to 17).
Abstract: Superconducting nanowires fabricated via carbon-nanotube templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: can a single phase-slip event occurring somewhere along the wire—during which the order-parameter fluctuates to zero—induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as a tool for evaluating and analyzing the mean switching time at a given value of current (smaller than the depairing critical current). The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the rather counterintuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way of unearthing and exploring the physics of nanoscale quantum tunneling of the one-dimensional collective quantum field associated with the superconducting order parameter.
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Romijn, J., Klapwijk, T. M., Renne, M. J., & Mooij, J. E. (1982). Critical pair-breaking current in superconducting aluminum strips far below Tc. Phys. Rev. B, 26(7), 3648–3655.
Abstract: Critical currents of narrow, thin aluminum strips have been measured as a function of temperature. For the smallest samples uniformity of the current density is obtained over a large temperature range. Hence the intrinsic limit on the currentcarrying capacity of the superconductor was measured outside the Ginzburg-Landau -regime. The experimental values are compared with recent theoretical predictions by Kupriyanov and Lukichev. An approximate method of solving their equations is given, the results of which agree with the exact solution to within 1%. Experimental data are in excellent agreement with theoretical predictions. The absolute values agree if one assumes a Ïl value of 4×10–16 Ωm2 with vF=1.3×106 m/s. This value for Ïl is the same as that found from measurements of the anomalous skin effect but differs from values extracted from size-effect-limited resistivity.
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Peltonen, J. T., Astafiev, O. V., Korneeva, Y. P., Voronov, B. M., Korneev, A. A., Charaev, I. M., et al. (2013). Coherent flux tunneling through NbN nanowires. Phys. Rev. B, 88(22), 220506 (1 to 5).
Abstract: We demonstrate evidence of coherent magnetic flux tunneling through superconducting nanowires patterned in a thin highly disordered NbN film. The phenomenon is revealed as a superposition of flux states in a fully metallic superconducting loop with the nanowire acting as an effective tunnel barrier for the magnetic flux, and reproducibly observed in different wires. The flux superposition achieved in the fully metallic NbN rings proves the universality of the phenomenon previously reported for InOx. We perform microwave spectroscopy and study the tunneling amplitude as a function of the wire width, compare the experimental results with theories, and estimate the parameters for existing theoretical models.
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Shah, N., Pekker, D., & Goldbart, P. M. (2008). Inherent stochasticity of superconductor-resistor switching behavior in nanowires. Phys. Rev. Lett., 101, 207001(1 to 4).
Abstract: We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.
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Pothier, H., Guéron, S., Birge, N. O., Esteve, D., & Devoret, M. H. (1997). Energy distribution function of quasiparticles in mesoscopic wires. Phys. Rev. Lett., 79(18), 3490–3493.
Abstract: We have measured with a tunnel probe the energy distribution function of Landau quasiparticles in metallic diffusive wires connected to two reservoir electrodes, with an applied bias voltage. The distribution function in the middle of a 1.5-μm-long wire resembles the half sum of the Fermi distributions of the reservoirs. The distribution functions in 5-μm-long wires are more rounded, due to interactions between quasiparticles during the longer diffusion time across the wire. From the scaling of the data with the bias voltage, we find that the scattering rate between two quasiparticles varies as <c9><203a>–2, where <c9><203a> is the energy transferred.
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