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Irwin, K. D. (2006). Thermodynamics of nonlinear bolometers near equilibrium. In Proc. 11th International Workshop on Low Temp. Detectors (Vol. 559, pp. 718–720).
Abstract: We present the first thermodynamically correct calculation of the noise in a simple nonlinear resistive bolometer or calorimeter operated out of equilibrium. The solution is rigorous only for first- and second-order deviations from equilibrium, and for the linear and quadratic terms of dissipative elements. In contrast, existing models of noise in resistive bolometers are based on the application of equilibrium theories to a system that is often nonlinear and out of equilibrium. We derive solutions applicable both in and out of steady state. The noise has power spectral density different from the equilibrium theory, and it has higher-order correlations and non-Gaussian characteristics. The results do not apply to non-Markovian hidden variables in the bolometer.
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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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Anthore, A., Pothier, H., & Esteve, D. (2003). Density of states in a superconductor carrying a supercurrent. Phys. Rev. Lett., 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, 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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Mooij, J. E., & Dekker, P. (1978). Static properties of two- and three-dimensional superconducting constrictions. J. Low Temp. Phys., 33(5/6), 551–576.
Abstract: Calculations have been performed on superconducting constrictions with hyperbolic geometry. Stationary Ginzburg-Landau equations are used, neglecting magneticfields. Emphasis is placed on the difference between two-and three -dimensional constrictions, which is related to the difference between uniform-thickness (UT) and variable-thickness (VT) superconducting microbridges. The width of the constriction w, normalized to the coherence length ξ is indicated by the parameter A (â‰<192> w/2ξ). It is found that small (A < 0.1), three-dimensional constrictions and VT bridges have a sinusoidal current-phase relation, linear temperature dependence of the critical current I c, and an I cR product (Ris the normal state resistance) equal to the Ambegaokar-Baratoff expression for Josephson junctions near T c. Two-dimensional constrictions behave as if they consist of an inner core with junction properties, in series with the films on both sides. The core consists of the region within a coherence length from the center of the structure. This size is temperature dependent. The core shows a sinusoidal current-phase relation and IcR according to Ambegaokar and Baratoff. For the whole constriction neither the phase difference nor R is finite. Two-dimensional constrictions have linear temperature dependence only when they are extremely narrow (A < 0.001). In two-dimensionalbridges the order parameter is depressed cover a distance of approximately the coherence length; in small three-dimensional constrictions this distance is approximately equal to the width. In narrow constrictions (and short microbridges) the current is not homogeneously distributedover the cross section. The effect has been investigated that occurs when in three-dimensional constrictions the width w is not much larger than l 0, the electron mean free path in the basic material. To this purpose a Ginzburg-Landau equation is derived from the Zaitsev boundary conditions which is valid for continuously changing material parameters. The critical current is decreased, but the IcR product remains constant.The results of the calculations are compared with experimental results for superconducting microbridges.
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