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Tinkham M, Free JU, Lau CN, Markovic N. Hysteretic I–V curves of superconducting nanowires. Phys. Rev. B. 2003;68:134515(1 to 7).
Abstract: Experimental I–V curves of superconducting MoGe nanowires show hysteresis for the thicker wires and none for the thinner wires. A rather quantitative account of these data for representative wires is obtained by numerically solving the one-dimensional heat flow equation to find a self-consistent distribution of temperature and local resistivity along the wire, using the measured linear resistance R(T) as input. This suggests that the retrapping current in the hysteretic I–V curves is primarily determined by heating effects, and not by the dynamics of phase motion in a tilted washboard potential as often assumed. Heating effects and thermal fluctuations from the low-resistance state to a high-resistance, quasinormal regime appear to set independent upper bounds for the switching current.
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Shah N, Pekker D, Goldbart PM. Inherent stochasticity of superconductor-resistor switching behavior in nanowires. Phys Rev Lett. 2008;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 NO, Esteve D, Devoret MH. Energy distribution function of quasiparticles in mesoscopic wires. Phys. Rev. Lett.. 1997;79(18):3490–3.
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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Pekker D, Shah N, Sahu M, Bezryadin A, Goldbart PM. Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires. Phys. Rev. B. 2009;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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Anthore A, Pothier H, Esteve D. Density of states in a superconductor carrying a supercurrent. Phys Rev Lett. 2003;90(12):127001 (1 to 4).
Abstract: We have measured the tunneling density of states (DOS) in a superconductor carrying a supercurrent or exposed to an external magnetic field. The pair correlations are weakened by the supercurrent, leading to a modification of the DOS and to a reduction of the gap. As predicted by the theory of superconductivity in diffusive metals, we find that this effect is similar to that of an external magnetic field.
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Romijn J, Klapwijk TM, Renne MJ, Mooij JE. Critical pair-breaking current in superconducting aluminum strips far below Tc. Phys Rev B. 1982;26(7):3648–55.
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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Sahu M, Bae M-H, Rogachev A, Pekker D, Wei T-C, Shah N, et al. Individual topological tunnelling events of a quantum field probed through their macroscopic consequences. Nature Phys. 2009;5:503–8.
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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Ovchinnikov YN, Varlamov AA. Fluctuation-dissipative phenomena in a narrow superconducting channel carrying current below critical. arXiv. 2009;0910.2659v1:1–4.
Abstract: The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is developed. These fluctuations result in the appearance of small but finite dissipation in the sample. The value of corresponding voltage is found as the function of temperature (close to transition temperature) and arbitrary bias current. It is demonstrated that the value of the activation energy (exponential factor in the Arrenius law) when current approaches to the critical one is proportional to (1-J/Jc)^(5/4). This result is in concordance with the one for the affine phenomenon of the Josephson current decay due to the thermal phase fluctuations, where the activation energy proportional (1-J/J_c)^(3/2)(the difference in the exponents is related to the additional current dependence of the order parameter). Found dependence of the activation energy on current explains the enormous discrepancy between the theoretically predicted before and the experimentally observed broadening of the resistive transition.
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Arutyunov KY, Ramos-Alvarez A, Semenov AV, Korneeva YP, An PP, Korneev AA, et al. Superconductivity in highly disordered NbN nanowires. Nanotechnol. 2016;27(47):47lt02 (1 to 8).
Abstract: The topic of superconductivity in strongly disordered materials has attracted significant attention. These materials appear to be rather promising for fabrication of various nanoscale devices such as bolometers and transition edge sensors of electromagnetic radiation. The vividly debated subject of intrinsic spatial inhomogeneity responsible for the non-Bardeen-Cooper-Schrieffer relation between the superconducting gap and the pairing potential is crucial both for understanding the fundamental issues of superconductivity in highly disordered superconductors, and for the operation of corresponding nanoelectronic devices. Here we report an experimental study of the electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. The temperature dependence of the critical current follows the textbook Ginzburg-Landau prediction for the quasi-one-dimensional superconducting channel I c approximately (1-T/T c)(3/2). We find that conventional models based on the the phase slip mechanism provide reasonable fits for the shape of R(T) transitions. Better agreement with R(T) data can be achieved assuming the existence of short 'weak links' with slightly reduced local critical temperature T c. Hence, one may conclude that an 'exotic' intrinsic electronic inhomogeneity either does not exist in our structures, or, if it does exist, it does not affect their resistive state properties, or does not provide any specific impact distinguishable from conventional weak links.
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Peltonen JT, Astafiev OV, Korneeva YP, Voronov BM, Korneev AA, Charaev IM, et al. Coherent flux tunneling through NbN nanowires. Phys Rev B. 2013;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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