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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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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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Sahu, M., Bae, M. - H., Rogachev, A., Pekker, D., Wei, T. - C., Shah, N., et al. (2009). Individual topological tunnelling events of a quantum field probed through their macroscopic consequences. Nature Phys., 5, 503–508.
Abstract: Phase slips are topological fluctuations that carry the superconducting order-parameter field between distinct current-carrying states. Owing to these phase slips, superconducting nanowires acquire electrical resistance. In such wires, it is well known that at higher temperatures phase slips occur through the process of thermal barrier-crossing by the order-parameter field. At low temperatures, the general expectation is that phase slips should proceed through quantum tunnelling events, which are known as quantum phase slips. However, resistive measurements have produced evidence both for and against the occurrence of quantum phase slips. Here, we report evidence for the observation of individual quantum phase-slip events in homogeneous ultranarrow wires at high bias currents. We accomplish this through measurements of the distribution of switching currents for which the width exhibits a rather counter-intuitive, monotonic increase with decreasing temperature. Importantly, measurements show that in nanowires with larger critical currents, quantum fluctuations dominate thermal fluctuations up to higher temperatures.
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Bennett, D. A., Schmidt, D. R., Swetz, D. S., & Ullom, J. N. (2014). Phase-slip lines as a resistance mechanism in transition-edge sensors. Appl. Phys. Lett., 104, 042602.
Abstract: The fundamental mechanism of resistance in voltage-biased superconducting films is poorly understood despite its importance as the basis of transition-edge sensors (TESs). TESs are utilized in state-of-the-art microbolometers and microcalorimeters covering a wide range of energies and applications. We present a model for the resistance of a TES based on phase-slip lines (PSLs) and compare the model to data. One of the model's predictions, discrete changes in the number of PSLs, is a possible explanation for the observed switching between discrete current states in localized regions of bias.
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Swetz, D. S., Bennett, D. A., Irwin, K. D., Schmidt, D. R., & Ullom, J. N. (2012). Current distribution and transition width in superconducting transition-edge sensors. Appl. Phys. Lett., 101, 242603.
Abstract: Present models of the superconducting-to-normal transition in transition-edge sensors (TESs) do not describe the current distribution within a biased TES. This distribution is complicated by normal-metal features that are integral to TES design. We present a model with one free parameter that describes the evolution of the current distribution with bias. To probe the current distribution experimentally, we fabricated TES devices with different current return geometries. Devices where the current return geometry mirrors current flow within the device have sharper transitions, thus allowing for a direct test of the current-flow model.Measurements from these devices show that current meanders through a TES low in the resistivetransition but flows across the normal-metal features by 40% of the normal-state resistance. Comparison of transition sharpness between device designs reveals that self-induced magnetic fields play an important role in determining the width of the superconducting transition.
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