Schmid A, Schön G. Linearized kinetic equations and relaxation processes of a superconductor near Tc. J Low Temp Phys. 1975;20(1-2):207–27.
Abstract: Starting from the equation of Gor'kov and Eliashberg in a form introduced by Eilenberger, we derive a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter. These equations resemble the Boltzmann equation and the Ginzburg-Landau equation, respectively, and they form a set of coupled equations. Two different modes can be distinguished, depending on whether the order parameter changes in magnitude or in phase. The equations are solved for the case of a stationary quasiparticle injection into a superconductor and the change in the electrochemical potential of the quasiparticles is calculated. Furthermore, we treat the problem of a current flowing perpendicular to a superconducting-normal interface in which a normal current is converted into a supercurrent, and we calculate the extra resistance of the interface.
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Mooij JE, Dekker P. Static properties of two- and three-dimensional superconducting constrictions. J Low Temp Phys. 1978;33(5/6):551–76.
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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Milostnaya I, Korneev A, Tarkhov M, Divochiy A, Minaeva O, Seleznev V, et al. Superconducting single photon nanowire detectors development for IR and THz applications. J Low Temp Phys. 2008;151(1-2):591–6.
Abstract: We present our progress in the development of superconducting single-photon detectors (SSPDs) based on meander-shaped nanowires made from few-nm-thick superconducting films. The SSPDs are operated at a temperature of 2–4.2 K (well below T c ) being biased with a current very close to the nanowire critical current at the operation temperature. To date, the material of choice for SSPDs is niobium nitride (NbN). Developed NbN SSPDs are capable of single photon counting in the range from VIS to mid-IR (up to 6 μm) with a record low dark counts rate and record-high counting rate. The use of a material with a low transition temperature should shift the detectors sensitivity towards longer wavelengths. We present state-of-the art NbN SSPDs as well as the results of our recent approach to expand the developed SSPD technology by the use of superconducting materials with lower T c , such as molybdenum rhenium (MoRe). MoRe SSPDs first were made and tested; a single photon response was obtained.
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Gershenzon EM, Gol'tsman GN, Elantiev AI, Karasik BS, Potoskuev SE. Intense electromagnetic radiation heating of electrons of a superconductor in the resistive state. Sov J Low Temp Phys. 1988;14(7):414–20.
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Florya IN, Korneeva YP, Mikhailov MY, Devizenko AY, Korneev AA, Goltsman GN. Photon counting statistics of superconducting single-photon detectors made of a three-layer WSi film. Low Temp Phys. 2018;44(3):221–5.
Abstract: Superconducting nanowire single-photon detectors (SNSPD) are used in quantum optics when record-breaking time resolution, high speed, and exceptionally low levels of dark counts (false readings) are required. Their detection efficiency is limited, however, by the absorption coefficient of the ultrathin superconducting film for the detected radiation. One possible way of increasing the detector absorption without limiting its broadband response is to make a detector in the form of several vertically stacked layers and connect them in parallel. For the first time we have studied single-photon detection in a multilayer structure consisting of three superconducting layers of amorphous tungsten silicide (WSi) separated by thin layers of amorphous silicon. Two operating modes of the detector are illustrated: an avalanche regime and an arm-trigger regime. A shift in these modes occurs at currents of ∼0.5–0.6 times the critical current of the detector.
This work was supported by technical task No. 88 for scientific research at the National Research University “Higher School of Economics,” Grant No. 14.V25.31.0007 from the Ministry of Education and Science of Russia, and the work of G. N. Goltsman was supported by task No. 3.7328.2017/VU of the Ministry of Education and Science of Russia.
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