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.

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.

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.

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.

Abstract: We investigate the role of electrothermal feedback in the operation of superconducting nanowire single-photon detectors (SNSPDs). It is found that the desired mode of operation for SNSPDs is only achieved if this feedback is unstable, which happens naturally through the slow electrical response associated with their relatively large kinetic inductance. If this response is sped up in an effort to increase the device count rate, the electrothermal feedback becomes stable and results in an effect known as latching, where the device is locked in a resistive state and can no longer detect photons. We present a set of experiments which elucidate this effect and a simple model which quantitatively explains the results.

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.

Abstract: The temperature dependence of the resistance of films of Al, Be, and NbC with small values of the electron mean free path L=1.5– 10 nm has been measured at 4.2–300 K. The resistance of all the films contains a T^2 contribution that is proportional to the residual resistance; this contribution has been attributed to the interference between the elastic electron scattering and the electron-phonon scattering. Fitting the data to the theory of the electron-phonon-impurity interference „M. Yu. Reiser and A. V. Sergeev, Zh. Eksp. Teor. Fiz. 92, 224 ~1987! @Sov. Phys. JETP 65, 1291 ~1987!#…, we obtain constants of nteraction of the electrons with transverse phonons, and estimate the contribution of this interaction to the electron dephasing rate in thin films of Au, Al, Be, Nb, and NbC. Our estimates are in a good agreement with the experimental data on the inelastic electronphonon scattering in these films. This indicates that the interaction of electrons with transverse phonons controls the electron-phonon relaxation rate in thin-metal films over a broad temperature range.

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 ρl value of 4×10–16 Ωm2 with vF=1.3×106 m/s. This value for ρl is the same as that found from measurements of the anomalous skin effect but differs from values extracted from size-effect-limited resistivity.

Abstract: Photoresponse of a superconducting film in the resistive state to pulsed radiation has been studied in the framework of a model assuming that two different effective temperatures can be assigned to the quasiparticle and phonon nonequilibrium distributions. The coupled electron-phonon-substrate system is described by a system of time-dependent energy-balance differential equations for effective temperatures. An analytical solution of the system is given and calculated voltage transients are compared with experimental photoresponse signals taking into account the radiation pulse shape and the time resolution of the readout electronics. It is supposed that a resistive state (vortices, fluxons, network of intergrain junctions, hot spots, phase slip centers) provides an ultrafast connection between electron temperature changes and changes of the film resistance and thus plays a minor role in the temporal evolution of the response. In accordance with experimental observations a two-component response was revealed from simulations. The slower component corresponds to a bolometric mechanism while the fast component is connected with the relaxation of the electron temperature. Calculated photoresponse transients are presented for different ratios of the electron and phonon specific heat, radiation pulse durations and fluences, and frequency band passes of registration electronics. From the amplitude of the bolometric component we determine the radiation energy absorbed in a film. This enables us to reveal an intrinsic electron-phonon scattering time even if it is much shorter than the time resolution of readout electronics. We analyze experimental voltage transients for NbN, YBa2Cu3O7, and TlBa2Ca2Cu3O9 superconducting films and find the electron-phonon interaction times at the transition temperatures of 17, 2.5, and 1.8 ps, respectively. The values are in reasonable agreement with data of other experiments.

Abstract: The electron–phonon interaction is strongly modified in conductors with a small value of the electron mean free path (impure metals, thin films). As a result, the temperature dependencies of both the inelastic electron scattering rate and resistivity differ significantly from those for pure bulk materials. Recent complex measurements have shown that modified dependencies are well described at K by the electron interaction with transverse phonons. At helium temperatures, available data are conflicting, and cannot be described by an universal model.

Abstract: We developed the model of the internal phonon bottleneck to describe the energy exchange between the acoustically soft ultrathin metal film and acoustically rigid substrate. Discriminating phonons in the film into two groups, escaping and nonescaping, we show that electrons and nonescaping phonons may form a unified subsystem, which is cooled down only due to interactions with escaping phonons, either due to direct phonon conversion or indirect sequential interaction with an electronic system. Using an amplitude-modulated absorption of the sub-THz radiation technique, we studied electron-phonon relaxation in ultrathin disordered films of tungsten silicide. We found an experimental proof of the internal phonon bottleneck. The experiment and simulation based on the proposed model agree well, resulting in τe−ph∼140–190 ps at TC=3.4K, supporting the results of earlier measurements by independent techniques.

Abstract: We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product qTl (qT is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14–30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/τe−ph∼Tn with the exponents n≈3.2–3.8. We found that in this temperature range τe−ph and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9–17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.

Abstract: We study the nonlinear response of current transport in a superconducting diffusive nanowire between normal reservoirs. We demonstrate theoretically and experimentally the existence of two different superconducting states appearing when the wire is driven out of equilibrium by an applied bias, called the global and bimodal superconducting states. The different states are identified by using two-probe measurements of the wire, and measurements of the local density of states with tunneling probes. The analysis is performed within the framework of the quasiclassical kinetic equations for diffusive superconductors.

Abstract: We use an external magnetic field to probe the detection mechanism of a superconducting nanowire single-photon detector. We argue that the hot belt model (which assumes partial suppression of the superconducting order parameter Δ across the whole width of the superconducting nanowire after absorption of the photon) does not explain observed weak-field dependence of the photon count rate (PCR) for photons with λ=450nm and noticeable decrease of PCR (with increasing the magnetic field) in a range of the currents for photons with wavelengths λ=450–1200nm. Found experimental results for all studied wavelengths can be explained by the vortex hot spot model (which assumes partial suppression of Δ in the area with size smaller than the width of the nanowire) if one takes into account nucleation and entrance of the vortices to the photon induced hot spot and their pinning by the hot spot with relatively large size and strongly suppressed Δ.

Abstract: We have investigated a series of superconducting bridges based on homogeneous amorphous WSi and MoSi films, with bridge widths w ranging from 2 to 1000μm and film thicknesses d∼4−6 and 100 nm. Upon decreasing the bridge widths below the respective Pearl lengths, we observe in all cases distinct changes in the characteristics of the resistive transitions to superconductivity. For each of the films, the resistivity curves R(B,T) separate at a well-defined and field-dependent temperature T∗(B) with decreasing the temperature, resulting in a dramatic suppression of the resistivity and a sharpening of the transitions with decreasing bridge width w. The associated excess conductivity in all the bridges scales as 1/w, which may suggest either the presence of a highly conducting region that is dominating the electric transport, or a change in the vortex dynamics in narrow enough bridges. We argue that this effect can only be observed in materials with sufficiently weak vortex pinning.