Relaxation Time of the Cooper-Pair Density in Tin

Peters, Robert A.; Meissner, Hans

doi:10.1103/physrevlett.30.965

Cited by 35 publications

(8 citation statements)

References 14 publications

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“…7 The same is true as regards nonequilibrium stationary states that are obtained by application of intense electromagnetic radiation. 8'9 Finally, we mention the observation 1~ 2 of finite voltage differences in a superconductor.…”

Section: Introductionmentioning

confidence: 71%

Linearized kinetic equations and relaxation processes of a superconductor near T c

1975

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Starting from the equation of Gor'kov and Eliashberg in a form introduced byEilenberger, we derive a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter. These equations resemble the Boltzmann equation and the Ginzburg-Landau equation, respectively, and they form a set of coupled equations. Two different modes can be distinguished, depending on whether the order parameter changes in magnitude or in phase. The equations are solved for the case of a stationary quasiparticle injection into a superconductor and the change in the electrochemical potential of the quasiparticles is calculated. Furthermore, we treat the problem of a current flowing perpendicular to a superconducting-normal interface in which a normal current is converted into a supercurrent, and we calculate the extra resistance of the interface.

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Section: Introductionmentioning

confidence: 71%

Linearized kinetic equations and relaxation processes of a superconductor near T c

1975

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“…Below T c there have been few measurements which have quantitatively probed the dynamical behavior of the order parameter. 9 Knowledge of the dynamics is important in the analysis of problems of technological interest such as transport in type-II superconductors and the normal-superconductor phase boundary. At the present time a simple time-dependent Ginzburg-Landau equation does not exist for the regime below T c .…”

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confidence: 99%

Superconducting Order-Parameter Fluctuations belowTc

Carlson

Goldman

1973

Phys. Rev. Lett.

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Measurements of the frequency-and wave-vector-dependent pair-field susceptibility have been carried out below the transition temperature of a superconductor using a tunneling technique. The results suggest that the dynamical equation of the order parameter below T c is something other than a diffusive time-dependent Ginzburg-Landau equation.In this Letter we report the first measurements of the frequency-and wave-vector-dependent pair-field susceptibility 1 ' 2 of a superconductor below its transition temperature. Previous measurements 3 have been confined to the case where the average pair field of one superconductor with transition temperature T c > was used to determine the pair-field susceptibility of a second metal with transition temperature T c in the temperature range T C . The two metals formed the electrodes of a thin-film tunnel junction, with an excess current in the dc I-V characteristic due to pair tunneling giving a direct measure of the imaginary part of the frequency-and wave-vector-dependent pair-field susceptibility of the normal electrode. The frequency and wave-vector dependence of this susceptibility were determined by measuring the voltage and magnetic-fie Id dependence of the excess current.When both metals are superconducting, the phases of the order parameters of the two electrodes are coupled by the tunneling interaction. The physical manifestations of this coupling are the usual ac and dc Josephson effects. A new effect is observed as the temperature is lowered below T c in the presence of a magnetic field applied in the plane of the junction, sufficient in magnitude to uncouple the order parameters and destroy the Josephson effect, but not greater than the critical field of either metal. Under these conditions, a contribution to the excess current-voltage characteristic is observed to develop in a continuous manner from features observed above T c which have been previously interpreted as the pair-field susceptibility. 2 ' 3 We interpret these low-temperature features of excess current as pair currents arising from the coupling between the order parameter in the electrode with transition temperature T c f and the fluctuating order parameter in the electrode with transition temperature T c . In analogy with the situation occurring above T c , we would expect the excess tunneling current to be a measure of the susceptibility of the low-transition-temperature electrode.In superconductors above T c fluctuations of the order parameter are governed by a diffusive time-dependent Ginzburg-Landau equation, 4 ' 5 which has been studied in previous measurements of the pair-field susceptibility. 3 These order-parameter fluctuations are also responsible for the precursive behavior in the electrical conductivity, 6 magnetic susceptibility, 7 and single-particle density of states 8 which have also been studied extensively in recent years. Below T c there have been few measurements which have quantitatively probed the dynamical behavior of the order parameter. 9 Knowledge of the dynamics is i...

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“…Elaborating on the consequences of such a coupling between density and momentum of the superfluid, one finds that a frequency-dependent contribution proportional to ra/(1-ito~'a) can be observed in the conductivity. 13 Quite generally, a frequency dependence of a transport coefficient is an indication of an internal relaxation process. There are cases known in hydrodynamics, 14 where the coefficient of second viscosity shows a considerable frequency dependence.…”

Section: Ds = ~De -~ Dn ---~-Dps -~ Ansmentioning

confidence: 99%

Phenomenological theory of dissipation in a superconductor

Schmid

1980

J Low Temp Phys

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Interest in nonequilibrium superconductivity in recent years has led to the discovery of numerous relaxation processes characteristic of superconductors. On the basis of the thermodynamic theory of irreversible processes, a systematic account is given of the transport coefficients and relaxation times of a superconductor. KINETIC EQUATIONSIn the past ten years, numerous relaxation processes characteristic of a superconductor have been discovered and discussed. Various relaxation times and transport coefficient have been measured in experiments and investigated in theoretical calculations. In this article, I wish to show how one can order systematically these relaxation processes and their transport coefficient on the basis of the thermodynamic theory of irreversible pro-1 cesses.For the case where the superfluid as well as the normal fluid may move without dissipation, Khalatnikov 2 was the first to elaborate on such a theory. In a superconductor, however, the normal fluid experiences friction with the lattice, which makes it necessary to introduce modifications.~ In addition, the superfluid momentum may be quite large.In the case of interest here, energy, particle number, and superfluid momentum are conserved quantities. This means that the thermodynamic properties of the system can be expressed formally by the following relation:

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Relaxation Time of the Cooper-Pair Density in Tin

Cited by 35 publications

References 14 publications

Linearized kinetic equations and relaxation processes of a superconductor near T c

Linearized kinetic equations and relaxation processes of a superconductor near T c

Superconducting Order-Parameter Fluctuations belowTc

Phenomenological theory of dissipation in a superconductor

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