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Submitted on 1 Jan 1978
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ORDER PARAMETER DYNAMICS AND
COLLECTIVE MODES IN MAGNETIC IMPURITY
DOPED SUPERCONDUCTOR
F. Aspen, A. Goldman
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8, Tome 39, aolit 1978, page C6-490
F.Aspen and A.M. Goldman
SchooZ of Physics and Astronomy, University of Minnesota MinneapoZis, Minnesota,USA 55455
R6sum6.- On a utilis6 la pdndtration des paires pour dtudier le comportement dynamique du paramstre d'ordre dans le supraconducteur Al(Er) contenant une impuretd magnstique. Nous utilisons les r6sul- tats pour explorer le domaine de validit6 d'un systsme coup16 d16quations qui d6crit le comportement dynamique du paramstre d'ordre et la fonction de distribution des quasiparticules dans un &tat hors d' Bquilibre.
Abstract.- Pair tunnelling has been used to probe the dynamics of the order parameter in the magnetic impurity doped superconductor Al(Er). The results have a bearing on the quantitative validity of the coupled system of equations for the dynamics of the order parameter and the non equilibrium quasiparticle distribution function.
Pair tunnelling in assymetric junctions can part which is greater than the imaginary (damping) be used to measure the imaginary part of the fre- part. In this regime, experiment and theory are on-
quency and wave-vector dependent pair field suscep- ly in qualitative agreement and further work is tibility /I/ x1'(w,k) of the lower Tc electrode of required /3/ to achieve a definitive test. The ad- the junction near its transition temperature. dition of magnetic impurities to the superconduc- xt'(w,k) is proportional to an excess tunnelling tor provides just such a test/4/. Impurities produ-
2eV 2e
current with w =
-
and k = T[d/~ +Q H
/2/.h ce pair-breaking which depends on the spin-flip
Here V is the dc bias across the junction and H is the magnetic field applied in its plane.iis the London penetration depth of the higher T electrode of the junction and d is the thickness of the elec- trode whose susceptibility is being determined.
Below Tc, the measured xt'(w,k) changes drama- tically from form found above Tc. In place of the quasi-Lorentzian diffusive peak associated with fluctuations in the order parameter modulus, one
finds a sharper peak at a voltage that increases with i~ =
I
(T-Tc) ITcl
.
A low frequency peak deve- lops which is rather insensitive to E =. For large enough E an additional peak (or step) appears in the I-V characteristic at a voltage near the gap v01 tage.
The sharp peak has been identified with a propagating mode in the phase of the order parame- ter.It is believed to be a consequence of the cou- pling of the order parameter to fluctuations in the quasiparticle distribution function cSf(w,k). This
coupling term, known as the "anomalous term", con- verts the phase fluctuation equation into a damped
wave equation. In terns of eigenfrequency solutions, the propagating mode frequency has a real (resonant)
'supported in part by the Department of Energy under contract EY-76-S-02-1569.
scattering time -c
.
This is an elastic scattering process which tends to suppress the anomalous termthus eventually resulting in an overdamping of the
propagating mode.
In our experiments, we have used Pb-Al(Er) junctions with a thin layer of oxidized A1 provi- ding the tunnelling barrier. The edges of the films are masked with Bi203, leaving a junction area of
(.251m)~. The range of normal state resistances is from .05 to .5
a.
There is a small linear leakage conductance which is usually 10-~-10-~ of the nor- mal conductance. From the I-V characteristics abo- ve Tc, where the theory is well understood,we candetermine Tc, the Pb gap, the diffusive constant D and the depairing parameter p. The diffusion constant is obtained from the graph of the relaxa- tion frequency vs. the square of the magnetic field while p is determined from,the graph of the rela-
xation frequency vs. temperature.T is determined by the onset of dc Josephson tunnelling.
In order to obtain the excess currents and xn(w,k) from the I-V charasteristics, the single particle and leakage currents must be subtracted.
The single particle current at fixed T and V de- pends only on the normal state resistance and the
Pb gap. First the normal state resistance is mea-
sured with both films in the normal state. Then
the Pb gap and leakage conductance are chosen so that the resulting excess current fits exactly the theoretical quasi-Lorentzian line shape. TO meet this criteria, we find the Pb gap is 1.36mV at 1.2K
and is unique to about 1 pV! The leakage conductan- ce is found to be a slowly varying linear function of temperature having a small positive (sometimes zero) TCR. Below Tc, parameters extrapolated from T > T are used to obtain the excess current.
We have attempted a general analysis xl'(w,k) to obtain the parameters characterizing the dyna- mics of the order parameter. This has involved a multiparameter fit to a function consisting of the
sum of quasi-Lorentzians and shifted quasi-lorent- zians to account for the contributions to x1'(w,k) from the modulus and phase of the order parameter. A smooth step function is used to account for the
feature near the aluminum gap. This analysis is in qualitative agreement with the theories except in the case of the longitudinal mode where the agree- ment is quantitative. However, because the functio- nal forms employed are a gross over simplification of those available theoretically, a comparison of experiment and theory using exact functions is ne- cessary. Such an analysis will be presented else- where.
The dominant effect of increasing magnetic impurities is to suppress the "anomalous term". The existence of a non-zero depairing parameter also leads to a gapless regime near T in which the propagating mode is overdamped. The latter is the major effect on the dynamics resulting from the suppression of the "anomalous" term.
The value of the depairing parameter is deter- mined from the reduction of the relaxation frequen- cy in the normal state from its p= 0 value. In Figure 1 we plot x8'(w,k) at fixed k for these films with different depairing parameters. It should be noted that the shape change usually associated with the propagating mode,is absent in the gapless regi- me. The widths of the gapless regimes as calculated from pare consistent with those observed. When superconductors with p # 0 are at sufficiently low temperatures that they once again have a gap and a propagating mode, the damping of the propa- gating mode is greater than that observed in the
p = 0 case for a metal with the same value of ~ k ~ , a result consistent with the predictions of theory. It would be of interest to extend these investiga-
tions to fully-gapless superconductors where the
time-dependent Ginzburg-Landau equation should
apply in the superconducting as well as the normal state.
Fig. 1 : Excess current-voltage characteristic (xl'(w,k)) for three Al(Er)-A1203-Pb junctions. A, B and C correspond to p = 0.002, 0.01 and 0.05 and to ~ k * = 26.9 vV, 20.4 vV, respectively. Temperatu- res range from T + 4 mK (labeled 1) to T
-
20 mK (labeled 7) in 4's steps.References
/l/ Carlson,R.V. and Goldman,A.M., J. Low Temp. Phys.
2
(1976) 67/2/ Scalapino,D.J., Phys. Rev. Lett.
2
(1977) 1052 /3/ Schmid,A. and Schsn, Phys. Rev. Lett.E
(1975)941, and Schsn,G., Doctoral Thesis, University of Dortmund (1976) unpublished
