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Bell, M., Sergeev, A., Mitin, V., Bird, J., Verevkin, A., & Gol’tsman, G. (2007). One-dimensional resistive states in quasi-two-dimensional superconductors: Experiment and theory. Phys. Rev. B, 76(9), 094521 (1 to 5).
Abstract: We investigate competition between one- and two-dimensional topological excitations—phase slips and vortices—in the formation of resistive states in quasi-two-dimensional superconductors in a wide temperature range below the mean-field transition temperature TC0. The widths w=100nm of our ultrathin NbN samples are substantially larger than the Ginzburg-Landau coherence length ξ=4nm, and the fluctuation resistivity above TC0 has a two-dimensional character. However, our data show that the resistivity below TC0 is produced by one-dimensional excitations—thermally activated phase slip strips (PSSs) overlapping the sample cross section. We also determine the scaling phase diagram, which shows that even in wider samples the PSS contribution dominates over vortices in a substantial region of current and/or temperature variations. Measuring the resistivity within 7 orders of magnitude, we find that the quantum phase slips can only be essential below this level.
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Boogaard, G. R., Verbruggen, A. H., Belzig, W., & Klapwijk T.M. (2004). Resistance of superconducting nanowires connected to normal-metal leads. Phys. Rev. B, 69, 220503(R)(1–4).
Abstract: We study experimentally the low temperature resistance of superconducting nanowires connected to normal metal reservoirs. Wefind that a substantial fraction of the nanowires is resistive, down to the lowest tempera-ture measured, indicative of an intrinsic boundary resistance due to the Andreev-conversion of normal current to supercurrent. The results are successfully analyzed in terms of the kinetic equations for diffusive superconductors.
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Bulaevskii, L. N., Graf, M. J., Batista, C. D., & Kogan, V. G. (2011). Vortex-induced dissipation in narrow current-biased thin-film superconducting strips. Phys. Rev. B, 83(14), 9.
Abstract: A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length ξ and of width w much narrower than the Pearl length Λâ‰<ab>wâ‰<ab>ξ. At high bias currents I*<I<Ic the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt forms along the vortex path and causes a transition of the entire strip into the normal state. We estimate I* to be roughly Ic/3. Furthermore, we argue that such “hot†vortex crossings are the origin of dark counts in photon detectors, which operate in the regime of metastable superconductivity at currents between I* and Ic. We estimate the rate of vortex crossings and compare it with recent experimental data for dark counts. For currents below I*, that is, in the stable superconducting but resistive regime, we estimate the amplitude and duration of voltage pulses induced by a single vortex crossing.
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Bulaevskii, L. N., Graf, M. J., & Kogan, V. G. (2012). Vortex-assisted photon counts and their magnetic field dependence in single-photon superconducting detectors. Phys. Rev. B, 85(1), 9.
Abstract: We argue that photon counts in a superconducting nanowire single-photon detector (SNSPD) are caused by the transition from a current-biased metastable superconducting state to the normal state. Such a transition is triggered by vortices crossing the thin and narrow superconducting strip from one edge to another due to the Lorentz force. Detector counts in SNSPDs may be caused by three processes: (a) a single incident photon with sufficient energy to break enough Cooper pairs to create a normal-state belt across the entire width of the strip (direct photon count), (b) thermally induced single-vortex crossing in the absence of photons (dark count), which at high-bias currents releases the energy sufficient to trigger the transition to the normal state in a belt across the whole width of the strip, and (c) a single incident photon of insufficient energy to create a normal-state belt but initiating a subsequent single-vortex crossing, which provides the rest of the energy needed to create the normal-state belt (vortex-assisted single-photon count). We derive the current dependence of the rate of vortex-assisted photon counts. The resulting photon count rate has a plateau at high currents close to the critical current and drops as a power law with high exponent at lower currents. While the magnetic field perpendicular to the film plane does not affect the formation of hot spots by photons, it causes the rate of vortex crossings (with or without photons) to increase. We show that by applying a magnetic field one may characterize the energy barrier for vortex crossings and identify the origin of dark counts and vortex-assisted photon counts.
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Ciulin, V., Carter, S. G., & Sherwin, M. S. (2004). Terahertz optical mixing in biased GaAs single quantum wells. Phys. Rev. B, 70(11), 115312–(1–6).
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Coumou, P. C. J. J., Driessen, E. F. C., Bueno, J., Chapelier, C., & Klapwijk, T. M. (2013). Electrodynamic response and local tunneling spectroscopy of strongly disordered superconducting TiN films. Phys. Rev. B, 88(18), 180505 (1 to 5).
Abstract: We have studied the electrodynamic response of strongly disordered superconducting TiN films using microwave resonators, where the disordered superconductor is the resonating element in a high-quality superconducting environment of NbTiN. We describe the response assuming an effective pair-breaking mechanism modifying the density of states and compare this to local tunneling spectra obtained using scanning tunneling spectroscopy. For the least disordered film (kFl=8.7, Rs=13Ω), we find good agreement, whereas for the most disordered film (kFl=0.82, Rs=4.3kΩ), there is a strong discrepancy, which signals the breakdown of a model based on uniform properties.
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Heslinga, D. R., Shafranjuk, S. E., van Kempen, H., & Klapwijk, T. M. (1994). Observation of double-gap-edge Andreev reflection at Si/Nb interfaces by point-contact spectroscopy. Phys. Rev. B, 49(15), 10484–10494.
Abstract: Andreev reflection point-contact spectroscopy is performed on a bilayer consisting of 50-nm degenerately doped Si backed with Nb. Due to the short mean free path both injection into and transport across the Si layer are diffusive, in contrast to the ballistic conditions prevailing in clean metal layers. Nevertheless a large Andreev signal is observed in the point-contact characteristics, not reduced by elastic scattering in the Si layer or by interface scattering, but only limited by the transmission coefficient of the metal-semiconductor point contact. Two peaks in the Andreev reflection probability are visible, marking the values of the superconducting energy gap at the interface on the Nb and Si sides. This interpretation is supported by a method of solving the Bogolubov equations analytically using a simplified expression for the variation of the order parameter close to the interface. This observation enables a comparison with theoretical predictions of the gap discontinuity in the proximity effect. It is found that the widely used de Gennes model does not agree with the experimental data.
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Huard, B., Pothier, H., Esteve, D., & Nagaev, K. E. (2007). Electron heating in metallic resistors at sub-Kelvin temperature. Phys. Rev. B, 76, 165426(1–9).
Abstract: In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time-dependent heating, an issue relevant for experiments in which current pulses are used, for instance, in time-resolved calorimetry experiments.
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Il’in, K. S., Ptitsina, N. G., Sergeev, A. V., Gol’tsman, G. N., Gershenzon, E. M., Karasik, B. S., et al. (1998). Interrelation of resistivity and inelastic electron-phonon scattering rate in impure NbC films. Phys. Rev. B, 57(24), 15623–15628.
Abstract: A complex study of the electron-phonon interaction in thin NbC films with electron mean free path l=2–13nm gives strong evidence that electron scattering is significantly modified due to the interference between electron-phonon and elastic electron scattering from impurities. The interference T2 term, which is proportional to the residual resistivity, dominates over the Bloch-Grüneisen contribution to resistivity at low temperatures up to 60 K. The electron energy relaxation rate is directly measured via the relaxation of hot electrons heated by modulated electromagnetic radiation. In the temperature range 1.5–10 K the relaxation rate shows a weak dependence on the electron mean free path and strong temperature dependence ∼Tn, with the exponent n=2.5–3. This behavior is explained well by the theory of the electron-phonon-impurity interference taking into account the electron coupling with transverse phonons determined from the resistivity data.
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Kardakova, A., Shishkin, A., Semenov, A., Goltsman, G. N., Ryabchun, S., Klapwijk, T. M., et al. (2016). Relaxation of the resistive superconducting state in boron-doped diamond films. Phys. Rev. B, 93(6), 064506.
Abstract: We report a study of the relaxation time of the restoration of the resistive superconducting state in single crystalline boron-doped diamond using amplitude-modulated absorption of (sub-)THz radiation (AMAR). The films grown on an insulating diamond substrate have a low carrier density of about 2.5×1021cm−3 and a critical temperature of about 2K. By changing the modulation frequency we find a high-frequency rolloff which we associate with the characteristic time of energy relaxation between the electron and the phonon systems or the relaxation time for nonequilibrium superconductivity. Our main result is that the electron-phonon scattering time varies clearly as T−2, over the accessible temperature range of 1.7 to 2.2 K. In addition, we find, upon approaching the critical temperature Tc, evidence for an increasing relaxation time on both sides of Tc.
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