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THE dc JOSEPHSON EFFECT FOR
SUPERCONDUCTING PROXIMITY SYSTEMS
N. Mori, S. Kodama, H. Ozaki
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppldment au no 8, Tome 39, aotir 1978, page C6-561
THE dc JOSEPHSON EFFECT FOR SUPERCONDUCTING P R O X I M I T Y SYSTEMS N. Mori, S. Kodama and H. Ozaki
Department of Electrical Engineering, Waseda University, Shinjuku, Tokyo, Japan
Rdsum6.- Nous Bvaluons dans la limite propre le courant continu Josephson maximum pour une jonction supraconducteur-metal normal-isolant-supraconducteur. Nos rdsultats sont cohdrents avec les expLrien- ces rdcentes et avec les theories existantes qui sont valables dans la limite sale. Nous Bvaluons aus- si le courant Josephson du sandwich de proximitd qui contient des impuretds magndtiques.
Abstract.- The maximum dc Josephon current is evaluated for a superconductor-norma1 metal-insulator- superconductor junction in the clean limit. The present results are consistent with recent experiments and with existing t h e o r i e sin the dirty limit. The Josephson current for a proximity sandwich containing magnetic impurities is also evaluated.
In recent years the maximum dc Josephson cur- rent J has been measured for tunnel junctions of a superconductor-normal metal-insulator-superconduc- tor (SNIS) structure/l,2/. The experimental results are in agreement with calculations based on the de Gennes model/3/ which is known to be valid in the dirty limit. However, the measurements have been performed on the samples which are not strictly dirty. In this paper we report computed results of J for a SNIS junction in the clean limit on the ba- sis of the McMillan model/4/.
In the SNIS junction under consideration the two S films are assumed to be identical superconduc- tors and the SN system to be well described by the McMillan model. A lifetime-braodening term associa-
ted with a coupling between S and N is given by I'i = sv ..o/8di, (i=S or N), where vF is the Fermi
F1
velocity, u the transmission coefficient at the SN interface and d the film thickness. First of all the order parameter
aph
and the gap function A(w) on each side of the SN proximity system should be all self-consistently determined for given TS andr
at each temperature T. Once and A(w) haveN
been determined J can be evaluated from the follo- wing equation/5,6/ :
where R is the junction resistance in the normal state and f(w) is the Fermi function. The terms PBCS(u,T) and PN(w,T) are given by
where A(T) is the temperature-dependent BCS energy gap in the counter S film and AN(w,T) is the fre- quency-dependent gap function on the N side at tem- perature T. As A (w,T) cannot be expressed in an
N
analytic form, we have to solve equation(1) numeri- cally.
Computed results for the temperature depen- dence of J are shown in figure 1 , where J is nor- malized by its value at T=O.
Fig. 1 : Normalized Josephson current vs. reduced temperature. A full curve is for a SIS junction, wh'le broken curves for SNIS junctions with
A t
=o.
A full curve obtained from equation (I) with repla- cing PN by PBCS shows the complete BCS (weak cou- pling) behaviour for the case of equal energy gaps. Broken curves are for the SNIS junction. It can be seen that the temperature dependence of J deviates from the BCS behaviour even for a thin normal metal (a large
r
) , and that the curve for a thick normalN
metal shows a slight upward curvature. These beha- viours are similar to those observed in the experi-
ments/1,2,7/ and to those predicted by the calcula- tions/l,2/ based on the de Gennes model. It is in- teresting to note that the theoretical descriptions starting from opposite limits give a qualitatively similar result. We have calculated the d dependen-
N
ce of J at T=O and have found that J decreases with increasing dN rapidly for small values of dN and slowly for large ones. This result is again consis- tent with a experiment/7/.
We also evaluate J at T = 0 for a SNIS junc- tion where the normal metal contains magnetic im- purities by the use of Kaiser and Zuckermann's theory/8/.In such a system there exists a large gapless region. In figure 2 we show J as a function of I? which is proportional to the impurity concen- tration.
References
/I/ Romagnan,J.P., Gilabert,A., Noiray,J.C. and Guyon,E.,Solid State Commun. (1974) 83 /2/ Rowel1,N.L. and Smith,H.J.T., Can. J. Phys.
54
(1976) 223
/3/ De Gennes,P.G., Rev. Mod. Phys.36 (1964) 225
141 McMillan,W.L., Phys. Rev.
175
(1968) 537 I51 Ambegaokar,V. and Baratoff,A., Phys. Rev. Lett.10 (1963) 486
-
161 Nam,S.B., Phys. Rev. E(1967) 470
171 Folens,G., Schwidta1,K. and Bruynseraede,Y., Thin Solid Films
24
(1976) 255/8/ Kaiser,A.B. and Zuckermann,M.J., Phys. Rev.
g
(1970) 229Fig. 2 : Reduction of Josephson current J at T = 0 by magnetic impurities. JO is the value of J for
r
= 0 ; AB is the order parameter of the bulk. Ener- gy gap w and transition temperature Tc are also shown (sge referencel81).With increasing
