Семенов, А. В., Девятов, И. А., Третьяков, И. В., Лобанов, Ю. В., Ожегов, Р. В., Петренко, Д. В., et al. (2011). Вывод уравнения типа уравнения гинзбурга-ландау для нанопроволоки вблизи критического магнитного поля. Ж. радиоэлектроники, 11, 4.
Abstract: Nonlinear Ginzburg-Landau equation for dirty supercondicting 1D wire is derived in the limit of high magnetic field.
В пределе больших магнитных полей выведено нелинейное уравнение Гинзбурга-Ландау, описывающее состояние одномерной «грязной» нанопроволоки.
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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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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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Ovchinnikov, Y. N., & Varlamov, A. A. (2009). Fluctuation-dissipative phenomena in a narrow superconducting channel carrying current below critical. arXiv, 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, K. Y., Ramos-Álvarez, A., Semenov, A. V., Korneeva, Y. P., An, P. P., Korneev, A. A., et al. (2016). Quasi-1-dimensional superconductivity in highly disordered NbN nanowires. arXiv:1602.07932v1 [cond-mat.supr-con].
Abstract: The topic of superconductivity in strongly disordered materials has attracted a significant attention. In particular vivid debates are related to the subject of intrinsic spatial inhomogeneity responsible for non-BCS relation between the superconducting gap and the pairing potential. Here we report experimental study of electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. We find that conventional models based on phase slip concept provide reasonable fits for the shape of the R(T) transition curve. Temperature dependence of the critical current follows the text-book Ginzburg-Landau prediction for quasi-one-dimensional superconducting channel Ic~(1-T/Tc)^3/2. Hence, one may conclude that the intrinsic electronic inhomogeneity either does not exist in our structures, or, if exist, does not affect their resistive state properties.
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