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Semenov, A. D.; Nebosis, R. S.; Gousev, Yu. P.; Heusinger, M. A.; Renk, K. F. |
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Analysis of the nonequilibrium photoresponse of superconducting films to pulsed radiation by use of a two-temperature model |
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1995 |
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Phys. Rev. B |
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Phys. Rev. B |
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52 |
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1 |
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581-590 |
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HEB, NbN phonon scecific heat, Cp |
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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. |
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903 |
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Tinkham, M.; Free, J. U.; Lau, C. N.; Markovic, N. |
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Hysteretic I–V curves of superconducting nanowires |
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2003 |
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Phys. Rev. B |
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68 |
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134515(1 to 7) |
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MoGe nanowires, self-heating effect |
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Experimental I–V curves of superconducting MoGe nanowires show hysteresis for the thicker wires and none for the thinner wires. A rather quantitative account of these data for representative wires is obtained by numerically solving the one-dimensional heat flow equation to find a self-consistent distribution of temperature and local resistivity along the wire, using the measured linear resistance R(T) as input. This suggests that the retrapping current in the hysteretic I–V curves is primarily determined by heating effects, and not by the dynamics of phase motion in a tilted washboard potential as often assumed. Heating effects and thermal fluctuations from the low-resistance state to a high-resistance, quasinormal regime appear to set independent upper bounds for the switching current. |
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918 |
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Pekker, David; Shah, Nayana; Sahu, Mitrabhanu; Bezryadin, Alexey; Goldbart, Paul M. |
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Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires |
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2009 |
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Phys. Rev. B |
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80 |
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214525 (1 to 17) |
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superconducting nanowire, phase-slip, order parameter, HEB distributed model, HEB model |
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Superconducting nanowires fabricated via carbon-nanotube templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: can a single phase-slip event occurring somewhere along the wire—during which the order-parameter fluctuates to zero—induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as a tool for evaluating and analyzing the mean switching time at a given value of current (smaller than the depairing critical current). The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the rather counterintuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way of unearthing and exploring the physics of nanoscale quantum tunneling of the one-dimensional collective quantum field associated with the superconducting order parameter. |
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Recommended by Klapwijk |
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923 |
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Romijn, J.; Klapwijk, T. M.; Renne, M. J.; Mooij, J. E. |
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Critical pair-breaking current in superconducting aluminum strips far below Tc |
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1982 |
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Phys. Rev. B |
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Phys. Rev. B |
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26 |
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7 |
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3648-3655 |
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superconducting nanowire |
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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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Huard, B.; Pothier, H.; Esteve, D.; Nagaev, K. E. |
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Electron heating in metallic resistors at sub-Kelvin temperature |
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Journal Article |
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2007 |
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Phys. Rev. B |
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Phys. Rev. B |
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76 |
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165426(1-9) |
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electron heating in resistor, HEB distributed model, HEB model, hot electrons |
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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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Recommended by Klapwijk as example for writing the article on the HEB model. |
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936 |
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Boogaard, G.R.; Verbruggen, A.H.; Belzig, W.; Klapwijk T.M. |
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Resistance of superconducting nanowires connected to normal-metal leads |
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Journal Article |
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2004 |
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Phys. Rev. B |
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Phys. Rev. B |
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69 |
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220503(R)(1-4) |
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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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RPLAB @ atomics90 @ |
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960 |
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Ptitsina N. G.; Chulkova G. M.; Il'in K. S.; Sergeev A. V.; Pochinkov F. S.; Gershenzon E. M. |
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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. |
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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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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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RPLAB @ phisix @ |
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Coumou, P. C. J. J.; Driessen, E. F. C.; Bueno, J.; Chapelier, C.; Klapwijk, T. M. |
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Electrodynamic response and local tunneling spectroscopy of strongly disordered superconducting TiN films |
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2013 |
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Phys. Rev. B |
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88 |
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18 |
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180505 (1 to 5) |
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strongly disordered superconducting TiN films, microwave resonators |
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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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Kardakova, A.; Shishkin, A.; Semenov, A.; Goltsman, G. N.; Ryabchun, S.; Klapwijk, T. M.; Bousquet, J.; Eon, D.; Sacépé, B.; Klein, T.; Bustarret, E. |
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Relaxation of the resistive superconducting state in boron-doped diamond films |
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2016 |
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Phys. Rev. B |
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Phys. Rev. B |
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93 |
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6 |
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064506 |
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boron-doped diamond films, resistive superconducting state, relaxation time |
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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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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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Electron energy relaxation in disordered superconducting NbN films |
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2020 |
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Phys. Rev. B |
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Phys. Rev. B |
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102 |
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5 |
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054501 (1 to 15) |
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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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