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Sidorova, M.; Semenov, Alexej D.; Hübers, H.-W.; Ilin, K.; Siegel, M.; Charaev, I.; Moshkova, M.; Kaurova, N.; Goltsman, G. N.; Zhang, X.; Schilling, A. |
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Title |
Electron energy relaxation in disordered superconducting NbN films |
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Journal Article |
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Year |
2020 |
Publication |
Phys. Rev. B |
Abbreviated Journal |
Phys. Rev. B |
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Volume |
102 |
Issue |
5 |
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054501 (1 to 15) |
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Keywords |
NbN SSPD, SNSPD, HEB, bandwidth, relaxation time |
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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. |
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2469-9950 |
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1266 |
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Author |
Parker, W. H. |
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Title |
Modified heating theory of nonequilibrium superconductors |
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Journal Article |
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Year |
1975 |
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Phys. Rev. B |
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12 |
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9 |
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3667-3672 |
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American Physical Society |
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mht_Parker_1975 |
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221 |
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Romijn, J.; Klapwijk, T. M.; Renne, M. J.; Mooij, J. E. |
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Title |
Critical pair-breaking current in superconducting aluminum strips far below Tc |
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Journal Article |
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Year |
1982 |
Publication |
Phys. Rev. B |
Abbreviated Journal |
Phys. Rev. B |
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Volume |
26 |
Issue |
7 |
Pages |
3648-3655 |
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Keywords |
superconducting nanowire |
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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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Recommended by Klapwijk |
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925 |
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Perrin, N.; Vanneste, C. |
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Title |
Response of superconducting films to a periodic optical irradiation |
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Journal Article |
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Year |
1983 |
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Phys. Rev. B |
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28 |
Issue |
9 |
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5150-5159 |
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sc_resp_Perrin_1983 |
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233 |
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Heslinga, D. R.; Shafranjuk, S. E.; van Kempen, H.; Klapwijk, T. M. |
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Title |
Observation of double-gap-edge Andreev reflection at Si/Nb interfaces by point-contact spectroscopy |
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Journal Article |
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Year |
1994 |
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Phys. Rev. B |
Abbreviated Journal |
Phys. Rev. B |
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Volume |
49 |
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15 |
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10484-10494 |
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Keywords |
Nb, Si, Nb-Si, Nb/Si, Si/Nb, Andreev reflection, point-contact spectroscopy |
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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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American Physical Society |
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1005 |
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Sergeev, A. V.; Semenov, A. D.; Kouminov, P.; Trifonov, V.; Goghidze, I. G.; Karasik, B. S.; Gol’tsman, G. N.; Gershenzon, E. M. |
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Title |
Transparency of a YBa2Cu3O7-film/substrate interface for thermal phonons measured by means of voltage response to radiation |
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Journal Article |
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Year |
1994 |
Publication |
Phys. Rev. B Condens. Matter. |
Abbreviated Journal |
Phys. Rev. B Condens. Matter. |
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Volume |
49 |
Issue |
13 |
Pages |
9091-9096 |
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Keywords |
YBCO films |
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Abstract |
The transparency of a film/substrate interface for thermal phonons was investigated for YBa2Cu3O7 thin films deposited on MgO, Al2O3, LaAlO3, NdGaO3, and ZrO2 substrates. Both voltage response to pulsed-visible and to continuously modulated far-infrared radiation show two regimes of heat escape from the film to the substrate. That one dominated by the thermal boundary resistance at the film/substrate interface provides an initial exponential decay of the response. The other one prevailing at longer times or smaller modulation frequencies causes much slower decay and is governed by phonon diffusion in the substrate. The transparency of the boundary for phonons incident from the film on the substrate and also from the substrate on the film was determined separately from the characteristic time of the exponential decay and from the time at which one regime was changed to the other. Taking into account the specific heat of optical phonons and the temperature dependence of the group velocity of acoustic phonons, we show that the body of experimental data agrees with acoustic mismatch theory rather than with the model that assumes strong diffusive scattering of phonons at the interface. |
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0163-1829 |
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PMID:10009690 |
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1648 |
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Verevkin, A. A.; Ptitsina, N. G.; Chulcova, G. M.; Gol'Tsman, G. N.; Gershenzon, E. M.; Yngvesson, K. S. |
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Title |
Determination of the limiting mobility of a two-dimensional electron gas in AlxGa1-xAs/GaAs heterostructures and direct measurement of the energy relaxation time |
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Journal Article |
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1996 |
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Phys. Rev. B Condens. Matter. |
Abbreviated Journal |
Phys. Rev. B Condens. Matter. |
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53 |
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12 |
Pages |
R7592-R7595 |
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2DEG, AlGaAs/GaAs heterostructures |
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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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0163-1829 |
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PMID:9982274 |
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1612 |
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Ptitsina, N. G.; Chulkova, G. M.; Il’in, K. S.; Sergeev, A. V.; Pochinkov, F. S.; Gershenzon, E. M.; Gershenson, M. E. |
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Electron-phonon interaction in disordered metal films: The resistivity and electron dephasing rate |
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1997 |
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Phys. Rev. B |
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Phys. Rev. B |
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56 |
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16 |
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10089-10096 |
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disordered metal films, electron-phonon interaction, electron dephasing rate, resistivity |
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The temperature dependence of the resistance of films of Al, Be, and NbC with small values of the electron mean free path l=1.5–10nm has been measured at 4.2–300 K. The resistance of all the films contains a T2 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 interaction 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 electron-phonon 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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0163-1829 |
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1766 |
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Il’in, K.S.; Ptitsina, N.G.; Sergeev, A.V.; Gol’tsman, G.N.; Gershenzon, E.M.; Karasik, B.S.; Pechen, E.V.; Krasnosvobodtsev, S.I. |
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Title |
Interrelation of resistivity and inelastic electron-phonon scattering rate in impure NbC films |
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Journal Article |
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1998 |
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Phys. Rev. B |
Abbreviated Journal |
Phys. Rev. B |
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Volume |
57 |
Issue |
24 |
Pages |
15623-15628 |
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Keywords |
NbC films |
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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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0163-1829 |
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1585 |
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Sergeev, A.; Mitin, V. |
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Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials |
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Journal Article |
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2000 |
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Phys. Rev. B. |
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Phys. Rev. B. |
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61 |
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9 |
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6041-6047 |
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disordered conductors, scattering potential, electron-phonon interaction |
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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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