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Submitted on 1 Jan 1978
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BASIS JOSEPHSON TUNNEL JUNCTION
PARAMETERS VARY STRONGLY WITH
TEMPERATURE BELOW Tc
S. Rudner, T. Claeson
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplPmenf au no 8, Tome 39,
aorif
1978, page
C6-604
BASIS JOSEPHSON TUNNEL JUNCTION
PARAMETERS
VARY STRONGLY WITH TEMPERATURE BELOW Tc
S.
Rudner and T. Claeson
Physics Dept., ChaZmers k i v . of Techn., Fack,
5-402 20
Gateborg, SwedenRbsumB.
-
On Btudie les variations de temp6rature des paramPtres d'une jonction tunnel.
Abstract.
-
Microwave reflection measurements on very small Pb tunnel junctions gave a strong
variation of the Josephson cos
+
amplitude between +I and -I
in an interval just below T
In the
c'
same range, the rf resistance displayed a sharp maximum.
A
smoother variation of the capacitance
with temperature and/or magnetic field (for tuning the plasma resonance) is interpreted as evidence
for the existence of a phase dependent parametric capacitance.
The often neglected temperature
dependence of
In particular, we want to emphasize the va-
riation in 5, the long disputed cos6 amplitude. The
original calculations /I/ gave 5
= + I ,but experi-
mental measurements /2/ consistently gave 5 =
-1.Later ,:heoretical work have tried to explain this
striking discrepancy, mainly by invoking a relaxa-
tion process
131.Our microwave reflection results,
displayed in figure 1 , show that
F
indeed equals -I
for temperatures up to above
0.9Tc. In a narrow
temperature interval, it then increases towards
+I
as the temperature is increased, until it decreases
very close to
T
the superconducting transition
c'
temperature. In the same temperature range, the
small signal rf resistance,
RJ,increases andpasses
through a maximum as if an additional tunnelling
channel were closed. The figure also shows that the
position of the maximum depends upon the magnitude
of the tunnelling current, 5.e. on the normal state
tunnelling resistance,
$.
This point, however,
needs further work to clarify.
1
basic tunnelling parameterswas studied indetail. We
found distinct variations in the parameters entering
the Josephson /I/ tunnel current equation
:m o -
I =
@I sin+
+
(1+
5cos
+)V / R ~
+
CdV/dt
J
where @ =
~in(m$/4~)/(n+/4~),
@is the magnetic flux
Fig.
I
:The upper part shows the temperature depen-
dence of 5, the cos$ amplitude, for two samples
with different values of
%.
The variation of IJ
(filled symbols) is also glven. The lower part dis-
plays ~
~
1
(open symbols) and C (filled circles,it
%
behaves similarly for the two samples).
-
- 100
*\
1 ~ h -
The capacitance varies with temperature too,
but much more smoothly than the previous two para-
meters, cf. figure
1.Here, we should stress thatat
the same time as the temperature is lowered, there
is an increase in the magnefic flux
4,
needed to
depress the Josephson plasma resonance to the micro-
wave frequency of the experiment. We interpret the
measured variation of the effective capacitance
(with a factor
2-3) as evidence for the existenceof
a phase dependent parametric capacitance of thetype
suggested by Zirmnermann/4/.
in the junction,
+0 =h/2e the quantized flux unit,
25 - 10 0
I is the maximum current (without a field) forpair
J
.--_
.
-..
=\.
transport between two superconductors with a phase
2 0 ---
difference 4, R is the shunt resistance determining
J
the quasiparticle tunnelling, Ccos
+
determines the
U
quasiparticle-pair interference contribution to the
tunnel current, and C is the capacitance.
Our results on the temperature variation of
t h e c o s $ amplitude a g r e e s u r p r i s i n g l y w e l l w i t h t h e v a l u e s o b t a i n e d w i t h i n two narrow temperature i n t e r - v a l s by Soerensen, Mygind, and Pedersen /5/ on a d i f f e r e n t superconductor, namely Sn. On t h e o t h e r hand, o u r r e s u l t s on RJ and C d i f f e r markedly from
t h e i r s , a s t h e y found a marginal change i n RJ and assumed a c o n s t a n t C.
Our experiments u t i l i z e d s m a l l , 18 pm x 18 pm, Pb/oxide/Pb t u n n e l j u n c t i o n s connected t o a micro- s t r i p t y p e t r a n s m i s s i o n l i n e 161. S p e c i a l c a r e was taken t o e l i m i n a t e resonances i n t h e s u b s t r a t e hol- d e r , and t h e frequency chosen (9.32 GHz) minimized s p u r i o u s r e f l e c t i o n s i n t h e system.
%
could be de- termined from t h e d c I - V c u r v ev i a
a b i a s t e e . I n t h i s i n v e s t i g a t i o n we used j u n c t i o n s w i t h RN i n t h e range 5-20 0 . A l l samples were good t u n n e l junctions w i t h n e g l i g i b l e leakage c u r r e n t s and IJ% p r o d u c t s of 1.5 mV a t 4.2 K.The r e f l e c t e d r a d i a t i o n
was
analysed i n a spectrum a n a l y s e r and t h e peak amplitude was plotted on an x-y r e c o r d e r a g a i n s t t h e a p p l i e d magnetic f i e l d . The r e s u l t of a t y p i c a l r e f l e c t i o n c o e f f i - c i e n t measurement i s shown i n f i g u r e 2. I n t h a t Fig. 2 : The r e f l e c t i o n c o e f f i c i e n t a t 9.3 GHz a s a f u n c t i o n of magnetic f i e l d f o r a s m a l l Pb/oxide/Pb tunnel j u n c t i o n a t 6.9 K.%
= 20 Q. Note t h e d i p due t o t h e plasma resonance. The c u r v e i s a l e a s t square f i t u s i n g g = 0.0887,5
= 0.0944, 5 = -0.771, R J' = 13.6 0 , and C = 6.23 pF.diagram we a l s o g i v e a t h e o r e t i c a l f i t of t h e power c o e f f i c i e n t , L vs 6 u s i n g t h e formula 161 :
5 = Mw/2eIJRJ, wl2n. t h e frequency, and C ' i n c l u d e s C and o t h e r r e a c t i v e s h u n t i n g elements t h a t can be s o r t e d o u t .
Note t h a t t h e d i p i n r e f l e c t e d power i s large because of t h e smallness of our j u n c t i o n s . T h i s f a c t , t o g e t h e r w i t h t h e good f i t d i s p l a y e d i n f i g u r e 2, means t h a t t h e parameters 5, RJ, and C c a n be d e t e r - mined w i t h r e l a t i v e l y small u n c e r t a i n t i e s . For t h e d a t a p r e s e n t e d i n f i g u r e 1 , t h e s e were e s t i m a t e d t o A < = k0.2, A(R J
/
%
) =+
0.3, and AC/C = k 0.06.Summarizing, we s t r e s s t h a t we have measured t h e b a s i c Josephson t u n n e l l i n g parameters RJ, 5 , and C i n t h e same j u n c t i o n w i t h i n a l a r g e temperature i n t e r v a l u t i l i z i n g one and t h e same experimental method. R v a r i e s s t r o n g l y w i t h i n t h e same tempera-
J
t u r e i n t e r v a l a s t h a t i n which 5 changes from posi- t i v e v a l u e s ( c l o s e t o T ) t o -1. The c o n s i d e r a b l e change i n C w i t h temperature a n d / o r magnetic f i e l d i s i n t e r p r e t e d a s a p a r a m e t r i c e f f e c t .
References
/ 1 / Josephson, B.D., Adv. Phys.
fi
(1965) 419/ 2 / Langenberg, D . N . , Rev. Phys. Appl.
9
(1974) 41 /3/ Deaver, B.S. Jr., Boone, B.G. and R i f k i n , R.Phys. L e t t .
57A
(1976) 186/4/ Zimmermann, J.E., Phys. L e t t .
42A
(1973) 375 /5/ Soerensen, O.H., Mygind, J . and Pedersen, N.F.,Phys. Rev. L e t t .
2
(1977) 1018161 Wahlsten, S . , Rudner, S. and Claeson, T., J. Appl. Phys. ( i n p r i n t ) ;
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