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Bulk mean field fluctuations in resistance of arrays of superconducting point contacts above Tc
Volume 29A, number 9
PHYSICS
LETTERS
F o r t h e s e e x p e r i m e n t a l c o n d i t i o n s t h e 1st maximum appeared for a different angle value t h a n t h e one m e n t i o n e d a b o v e ( s e e fig. 1) w h i c h gives a new value for the fluctuation temperature, n a m e l y T = T c - 10oC. T h e f a c t t h a t none of K o c i n s k i ' s m i n i m a h a s b e e n o b s e r v e d can b e e x p l a i n e d by t h e a s s u m p t i o n that the differential cross-section for neutron c r i t i c a l s c a t t e r i n g i s a s u m of two t e r m s , t h e f i r s t one g i v e n by van H o v e and t h e s e c o n d one by K o c i n s k i , i . e . [3]. R Cl ~ 1 +'C2 f s i n ~ r l s i n ~ 2 r l dr. (3) ~ 0
28 July 1969
After performing some theoretical calculations a r e p o r t g i v i n g f u l l i n t e r p r e t a t i o n of t h e s e and other experimental results will be published.
References 1. J.Kocinski, Aeta Phys. Polon. 30 (1966) 591. 2. K. Blinowski and R. Ciszewski, Phys. Letters 28A (1968) 389. 3. J. Kocinski and K. Wentowska, Acta Phys. Poton., to be published.
+~2
* * * * *
BULK ARRAYS
MEAN F I E L D F L U C T U A T I O N S IN R E S I S T A N C E OF OF S U P E R C O N D U C T I N G POINT CONTACTS ABOVE Tc T. D. CLARK*
Philips Research Laboratories, Eindhoven, Netherlands and D. I t T I L L E Y
Physics Department, Unive~'sity of Essex, Colchester, Essex, UK Received 30 May 1969
The resistance of ball a r r a y s increases according to the "bulk n Curie-Weiss law. We attribute the inc r e a s e to fluctuations in the contact regions.
A b o v e T c t h e r e s i s t a n c e of a d i s o r d e r e d superconducting region should satisfy R / ( R N - R ) = A -1 [(T - T c ) / T c ] n with n = 1 f o r a t h i n f i l m , a n d n = ½ f o r a b u l k r e g i o n [1]. We b e l i e v e we h a v e o b s e r v e d t h e b u l k b e h a v i o u r , 1 n = ~, in p o i n t c o n t a c t a r r a y s . Fig. 1 s h o w s t h e top of t h e r e s i s t i v e t r a n s i t i o n of a c y l i n d r i c a l a r r a y of 1 0 0 ~ m tin b a l l s , l e n g t h 5 m m and c r o s s s e c t i o n 4 m m . B e l o w 3.7OK a " p h a s e s l i p " t a i l ~ lOK in width i s s e e n (2) and f o r T << T c a w e l l d e f i n e d s u p e r c u r r e n t d e v e l o p e d . ( 4 7 ~ A at 1.57OK). T h e e x p e r i m e n t a l p o i n t s up to t h e i n f l e x i o n at a b o u t 6 . 5 ° K in fig. 1 fit t h e " b u l k " C u r i e - W e i s s law. F i g . 2 s h o w s ~ / ( R N - R ) ] 2 p l o t t e d v e r s u s T. T h e d a t a a r e p l o t t e d l o g a r i t h m i c a l l y in fig. 3. T h e p o i n t s b e l o w 3 . 8 4 ° K in fig. 3 r i s e a b o v e t h e * Permanent address: Mullard Research Laboratories, Salfords, Redhill, Surrey, UK. 514
950
R~
~45
~O@
OBSBOeI~Oe
lO ~
BeeOg
Q
°e go
935
4:0
~o
e:o
7;0
~.o
9o 3-.K 15o
Fig. I. Resistancefrom Tc to onset of phononlimited
resistance.
Volume 29A, number 9
PHYSICS LETTERS OQO O
S~ Q
~o
O
•
Q
O
O
x
o
O O
o I eco~ °
.b Fig. 2. R2/(R N - R ) 2 versus T, assuming R N = 945.9 ~ . line e x t r a p o l a t e d f r o m the h i g h e r t e m p e r a t u r e v a l u e s , p r e s u m a b l y b e c a u s e the r e s i s t a n c e v a l u e s do not drop c a t a s t r o p h i c a l l y to z e r o but join s m o o t h l y to the phase slip tail. T h e s t r a i g h t line fit in fig. 2, and the log. plot in fig. 3, s e e m good e v i d e n c e that we a r e o b s e r v i n g bulk fluctuations. The data cannot be f i t t e d to the two d i m e n s i o n a l law, n = 1. An R N v a l u e can be found such that R / ( R N - R ) is l i n e a r i n T ; but then the line e x t r a p o l a t e s through 2.85OK, well below T c. F o r any r e a s o n a b l e value of R N (and Tc) the log. log plot has slope < 0.5.
In p r i n c i p l e the r e s i d u e of the high t e m p e r a t u r e change in r e s i s t a n c e should be s u b t r a c t e d . We can o v e r e s t i m a t e t h i s c o r r e c t i o n by a s s u m i n g that the high t e m p e r a t u r e p a r t continues down with the slope at the point of inflection. T h i s c o r r e c t i o n i s l e s s than the e x p e r i m e n t a l s c a t t e r in fig. 2 b et w een 4OK and 5OK, but b e c o m e s m o r e i m p o r t a n t above 5°K. H o w e v e r , the C u r i e - W e i s s law does a p p e a r to fit t h e data up to 6.5OK s u g g e s t i n g that we have g r o s s l y o v e r e s t i m a t e d t h i s effect. We have s e e n s i m i l a r i n c r e a s e s of r e s i s t a n c e a b o v e Tc many t i m e s in single point c o n t a c t s and a r r a o y s . The m a r k e d " s u b - h a r m o n i c " s t r u c t u r e in the I v e r s u s V c h a r a c t e r i s t i c s of a r r a y s (3) s u g g e s t s that the c o n t a c t s a r e d i s o r d e r e d m e t a l l i c r e g i o n s (4), and we p r e s s u m e the f l u c t u a t i o n s a r e o c c u r r i n g in the contacts. The sl o p e of the line in fig. 2 g i v e s A = 10-3. Taking a o ~ t ( / m v F = 1 0 - 8 c m , ~o = 2.3 × × 10-5 c m (5) [A = a~/~o½/~[1], we get m e a n f r e e path l ~ 7 × 10 -.8 cm. C o n s e q u e n t l y (~ol) 2~ ~ 1.3 × 10 -6 c m , and t h i s c o h e r e n c e length is l e s s than the likely s i z e of the co n t act s. We would like to thank M i s s G. t e r H a a r and Mr. J. de Jongh f o r t h e i r a s s i s t a n c e in p e r f o r m i n g these experiments.
10
1< F i g . 3. l n ( i ~ / ( R N - R ) )
28 July 1969
References 1. L.D. Kadanoff and G. Laramore, Phys. Rev. 175 (1968) 579. 2. T.D. Clark and D. R. Tflley, Phys. Letters 28A (1968) 62. 3. T.D. Clark, Phys. Letters 27A (1968) 585. 4. J.M. Rowell and W. L. Feldman, Phys. Rev. 172 (1968) 393. 5. P. G. DeGennes, Superconductivity of metals and alloys (Benjamin) 24.
1:O T-T¢ versus ln(T-Tc),
with T c =
= 3.72OK. * * * * *
515
PHYSICS
LETTERS
F o r t h e s e e x p e r i m e n t a l c o n d i t i o n s t h e 1st maximum appeared for a different angle value t h a n t h e one m e n t i o n e d a b o v e ( s e e fig. 1) w h i c h gives a new value for the fluctuation temperature, n a m e l y T = T c - 10oC. T h e f a c t t h a t none of K o c i n s k i ' s m i n i m a h a s b e e n o b s e r v e d can b e e x p l a i n e d by t h e a s s u m p t i o n that the differential cross-section for neutron c r i t i c a l s c a t t e r i n g i s a s u m of two t e r m s , t h e f i r s t one g i v e n by van H o v e and t h e s e c o n d one by K o c i n s k i , i . e . [3]. R Cl ~ 1 +'C2 f s i n ~ r l s i n ~ 2 r l dr. (3) ~ 0
28 July 1969
After performing some theoretical calculations a r e p o r t g i v i n g f u l l i n t e r p r e t a t i o n of t h e s e and other experimental results will be published.
References 1. J.Kocinski, Aeta Phys. Polon. 30 (1966) 591. 2. K. Blinowski and R. Ciszewski, Phys. Letters 28A (1968) 389. 3. J. Kocinski and K. Wentowska, Acta Phys. Poton., to be published.
+~2
* * * * *
BULK ARRAYS
MEAN F I E L D F L U C T U A T I O N S IN R E S I S T A N C E OF OF S U P E R C O N D U C T I N G POINT CONTACTS ABOVE Tc T. D. CLARK*
Philips Research Laboratories, Eindhoven, Netherlands and D. I t T I L L E Y
Physics Department, Unive~'sity of Essex, Colchester, Essex, UK Received 30 May 1969
The resistance of ball a r r a y s increases according to the "bulk n Curie-Weiss law. We attribute the inc r e a s e to fluctuations in the contact regions.
A b o v e T c t h e r e s i s t a n c e of a d i s o r d e r e d superconducting region should satisfy R / ( R N - R ) = A -1 [(T - T c ) / T c ] n with n = 1 f o r a t h i n f i l m , a n d n = ½ f o r a b u l k r e g i o n [1]. We b e l i e v e we h a v e o b s e r v e d t h e b u l k b e h a v i o u r , 1 n = ~, in p o i n t c o n t a c t a r r a y s . Fig. 1 s h o w s t h e top of t h e r e s i s t i v e t r a n s i t i o n of a c y l i n d r i c a l a r r a y of 1 0 0 ~ m tin b a l l s , l e n g t h 5 m m and c r o s s s e c t i o n 4 m m . B e l o w 3.7OK a " p h a s e s l i p " t a i l ~ lOK in width i s s e e n (2) and f o r T << T c a w e l l d e f i n e d s u p e r c u r r e n t d e v e l o p e d . ( 4 7 ~ A at 1.57OK). T h e e x p e r i m e n t a l p o i n t s up to t h e i n f l e x i o n at a b o u t 6 . 5 ° K in fig. 1 fit t h e " b u l k " C u r i e - W e i s s law. F i g . 2 s h o w s ~ / ( R N - R ) ] 2 p l o t t e d v e r s u s T. T h e d a t a a r e p l o t t e d l o g a r i t h m i c a l l y in fig. 3. T h e p o i n t s b e l o w 3 . 8 4 ° K in fig. 3 r i s e a b o v e t h e * Permanent address: Mullard Research Laboratories, Salfords, Redhill, Surrey, UK. 514
950
R~
~45
~O@
OBSBOeI~Oe
lO ~
BeeOg
Q
°e go
935
4:0
~o
e:o
7;0
~.o
9o 3-.K 15o
Fig. I. Resistancefrom Tc to onset of phononlimited
resistance.
Volume 29A, number 9
PHYSICS LETTERS OQO O
S~ Q
~o
O
•
Q
O
O
x
o
O O
o I eco~ °
.b Fig. 2. R2/(R N - R ) 2 versus T, assuming R N = 945.9 ~ . line e x t r a p o l a t e d f r o m the h i g h e r t e m p e r a t u r e v a l u e s , p r e s u m a b l y b e c a u s e the r e s i s t a n c e v a l u e s do not drop c a t a s t r o p h i c a l l y to z e r o but join s m o o t h l y to the phase slip tail. T h e s t r a i g h t line fit in fig. 2, and the log. plot in fig. 3, s e e m good e v i d e n c e that we a r e o b s e r v i n g bulk fluctuations. The data cannot be f i t t e d to the two d i m e n s i o n a l law, n = 1. An R N v a l u e can be found such that R / ( R N - R ) is l i n e a r i n T ; but then the line e x t r a p o l a t e s through 2.85OK, well below T c. F o r any r e a s o n a b l e value of R N (and Tc) the log. log plot has slope < 0.5.
In p r i n c i p l e the r e s i d u e of the high t e m p e r a t u r e change in r e s i s t a n c e should be s u b t r a c t e d . We can o v e r e s t i m a t e t h i s c o r r e c t i o n by a s s u m i n g that the high t e m p e r a t u r e p a r t continues down with the slope at the point of inflection. T h i s c o r r e c t i o n i s l e s s than the e x p e r i m e n t a l s c a t t e r in fig. 2 b et w een 4OK and 5OK, but b e c o m e s m o r e i m p o r t a n t above 5°K. H o w e v e r , the C u r i e - W e i s s law does a p p e a r to fit t h e data up to 6.5OK s u g g e s t i n g that we have g r o s s l y o v e r e s t i m a t e d t h i s effect. We have s e e n s i m i l a r i n c r e a s e s of r e s i s t a n c e a b o v e Tc many t i m e s in single point c o n t a c t s and a r r a o y s . The m a r k e d " s u b - h a r m o n i c " s t r u c t u r e in the I v e r s u s V c h a r a c t e r i s t i c s of a r r a y s (3) s u g g e s t s that the c o n t a c t s a r e d i s o r d e r e d m e t a l l i c r e g i o n s (4), and we p r e s s u m e the f l u c t u a t i o n s a r e o c c u r r i n g in the contacts. The sl o p e of the line in fig. 2 g i v e s A = 10-3. Taking a o ~ t ( / m v F = 1 0 - 8 c m , ~o = 2.3 × × 10-5 c m (5) [A = a~/~o½/~[1], we get m e a n f r e e path l ~ 7 × 10 -.8 cm. C o n s e q u e n t l y (~ol) 2~ ~ 1.3 × 10 -6 c m , and t h i s c o h e r e n c e length is l e s s than the likely s i z e of the co n t act s. We would like to thank M i s s G. t e r H a a r and Mr. J. de Jongh f o r t h e i r a s s i s t a n c e in p e r f o r m i n g these experiments.
10
1< F i g . 3. l n ( i ~ / ( R N - R ) )
28 July 1969
References 1. L.D. Kadanoff and G. Laramore, Phys. Rev. 175 (1968) 579. 2. T.D. Clark and D. R. Tflley, Phys. Letters 28A (1968) 62. 3. T.D. Clark, Phys. Letters 27A (1968) 585. 4. J.M. Rowell and W. L. Feldman, Phys. Rev. 172 (1968) 393. 5. P. G. DeGennes, Superconductivity of metals and alloys (Benjamin) 24.
1:O T-T¢ versus ln(T-Tc),
with T c =
= 3.72OK. * * * * *
515