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Bardeen, J; Mattis, D. C. |
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Theory of the anomalous skin effect in normal and superconducting metals |
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1958 |
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Phys. Rev. |
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Phys. Rev. |
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111 |
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2 |
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412-417 |
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local dirty limit, complex conductivity, HEB |
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Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films. |
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937 |
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Vercruyssen, N.; Verhagen, T. G. A.; Flokstra, M. G.; Pekola, J. P.; Klapwijk, T. M. |
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Title |
Evanescent states and nonequilibrium in driven superconducting nanowires |
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Journal Article |
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Year |
2012 |
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Phys. Rev. B |
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Phys. Rev. B |
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85 |
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224503(1-10) |
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Al HEB, Al superconducting nanowire, global state, bimodal state, quasiclassical kinetic equations, Usadel equation |
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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. |
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898 |
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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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Keywords |
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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Huard, B.; Pothier, H.; Esteve, D.; Nagaev, K. E. |
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Title |
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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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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2020 |
Publication |
Phys. Rev. B |
Abbreviated Journal |
Phys. Rev. B |
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Volume |
102 |
Issue |
5 |
Pages |
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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