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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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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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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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Ptitsina N. G., Chulkova G. M., Il'in K. S., Sergeev A. V., Pochinkov F. S., & Gershenzon E. M. (1997). Superconductivity has been found in a number of new compounds between the non-superconducting transition elements and nonmetals such as Si, Ge, and Te. These findings have suggested possible criteria for superconductivity in both elements and compounds. Phys. Rev. B, 56(16).
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.
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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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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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Sergeev, A., & Mitin, V. (2000). Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials. Phys. Rev. B., 61(9), 6041–6047.
Abstract: Employing the Keldysh diagram technique, we calculate the electron-phonon energy relaxation rate in a conductor with the vibrating and static δ-correlated random electron-scattering potentials. If the scattering potential is completely dragged by phonons, this model yields the Schmid’s result for the inelastic electron-scattering rate τ−1e−ph. At low temperatures the effective interaction decreases due to disorder, and τ−1e−ph∝T4l (l is the electron mean-free path). In the presense of the static potential, quantum interference of numerous scattering processes drastically changes the effective electron-phonon interaction. In particular, at low temperatures the interaction increases, and τ−1e−ph∝T2/l. Along with an enhancement of the interaction, which is observed in disordered metallic films and semiconducting structures at low temperatures, the suggested model allows us to explain the strong sensitivity of the electron relaxation rate to the microscopic quality of a particular film.
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Zhang, J., Słysz, W., Pearlman, A., Verevkin, A., Sobolewski, R., Okunev, O., et al. (2003). Time delay of resistive-state formation in superconducting stripes excited by single optical photons. Phys. Rev. B, 67(13), 132508 (1 to 4).
Abstract: We have observed a 65(±5)-ps time delay in the onset of a resistive-state formation in 10-nm-thick, 130-nm-wide NbN superconducting stripes exposed to single photons. The delay in the photoresponse decreased to zero when the stripe was irradiated by multi-photon (classical) optical pulses. Our NbN structures were kept at 4.2 K, well below the material’s critical temperature, and were illuminated by 100-fs-wide optical pulses. The time-delay phenomenon has been explained within the framework of a model based on photon-induced generation of a hotspot in the superconducting stripe and subsequent, supercurrent-assisted, resistive-state formation across the entire stripe cross section. The measured time delays in both the single-photon and two-photon detection regimes agree well with theoretical predictions of the resistive-state dynamics in one-dimensional superconducting stripes.
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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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Verevkin, A. A., Ptitsina, N. G., Chulcova, G. M., Gol'Tsman, G. N., Gershenzon, E. M., & Yngvesson, K. S. (1996). Determination of the limiting mobility of a two-dimensional electron gas in AlxGa1-xAs/GaAs heterostructures and direct measurement of the energy relaxation time. Phys. Rev. B Condens. Matter., 53(12), R7592–R7595.
Abstract: We present results for a method to measure directly the energy relaxation time (τe) for electrons in a single AlxGa1−xAs/GaAs heterojunction; measurements were performed from 1.6 to 15 K under quasiequilibrium conditions. We find τeαT−1 below 4 K, and τe independent of T above 4 K. We have also measured the energy-loss rate, ⟨Q⟩, by the Shubnikov-de Haas technique, and find ⟨Q⟩α(T3e−T3) for T<~4.2 K; Te is the electron temperature. The values and temperature dependence of τe and ⟨Q⟩ for T<4 K agree with calculations based on piezoelectric and deformation potential acoustic phonon scattering. At 4.2 K, we can also estimate the momentum relaxation time, τm, from our measured τe. This leads to a preliminary estimate of the phonon-limited mobility at 4.2 K of μ=3×107 cm2/Vs (ns=4.2×1011 cm−2), which agrees well with published numerical calculations, as well as with an earlier indirect estimate based on measurements on a sample with much higher mobility.
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