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Induced superconductivity in germanium films
Volume 33A, number 8
PHYSICS
• 0,~
0.2
, ~c
L 16
' 22
2'8
' ~c
' ~,0
Fig. 2. The dependence of the critical pump parameter ~_c versus the reflection coefficient r 2 for 72 = 0.5 (hc ~ 11.0 is the corresponding critical pump parameter for the model with distributed losses). b o u n d a r y of D - d i a g r a m s e r v e s the p a r a m e t r i c c u r v e d e r i v e d f r o m eq. (2) f o r fl = i ~ and i a q ( ~ ) = = in((2) +w (~2). T h e c o m p a r i s o n of the f o u r d i f f e r e n t p a r a m e t r i c c u r v e s C1, C2, C 3 and C(r (fig. 1) p e r m i t s to e s t a b l i s h that the p o s i t i o n of the c e n t r e of the u n s t a b l e m o d e d o m a i n , i t s d i m e n s i o n s , as w e l l a s the c r i t i c a l p u m p p a r a m e t e r ;t c d e p e n d s on the d e g r e e of the f i e l d c h a n g e (r -2) in the
INDUCED
SUPERCONDUCTIVITY
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28 December 1970
c a v i t y . T h e r e a s o n i s that the p r o b a b i l i t y of the m u l t i - p h o t o n (in p a r t i c u l a r , f o u r - p h o t o n [4]) i n t e r a c t i o n r e s p o n s i b l e f o r the o c c u r r e n c e of the i n s t a b i l i t y i n v e s t i g a t e d is d e p e n d e n t on the f r e q u e n c y d e t u n i n g (2 of the w e a k f i e l d f r e q u e n c i e s (~2o ± ~ ) f r o m the s t r o n g f i e l d f r e q u e n c y P-O and on i t s i n t e n s i t y E 2. The r e l i e f E 2 ( z ) p r o d u c e s the i n h o m o g e n e o u s b r o a d e n i n g of the r e s p o n s e at the f r e q u e n c y of the w e a k f i e l d w h i c h , in the long run, l e a d s to i n c r e a s i n g >,c a s r 2 ~ 0 ( s e e fig. 2). T h e a u t h o r e x p r e s s e s his thanks to P r o f e s s o r V. I. T a l a n o v f o r his v a l u a b l e r e m a r k s and s t e a d y i n t e r e s t for the p a p e r and a l s o P r o f e s s o r s V. I. B e s p a l o v and Ya. I. Khanin f o r u s e f u l d i s c u s s i o n .
References [1] H. Risken and K. Nummedai, Phys. Letters 26A (1968) 275. [2] N. D. Milovsky, Izv. VUZov Radiofiz. 13 {1970). [3] N.D. Milovsky, Izv. VUZov Radiofiz. 7 0964) 1095. [4] V. M. Arutyunyan, E.G. Kanetsan and V. O. Chaltykyan, J E T P 59(1970) 195.
IN
GERMANIUM
FILMS
*
S. G. LIPSON and M. M. S T U P E L Department of P h y s i c s , Technion - I s r a e l Institute of Technology, Haifa, Israel Received 25 October 1970
The voltage-current characteristics of films of Ge, sandwiched between Sn and Sn, and sandwiched between Sn and A1, have been measured at helium temperatures.
In a n u m b e r of e x p e r i m e n t s at h e l i u m t e m p e r a t u r e s we h a v e i n v e s t i g a t e d the t e m p e r a t u r e and c u r r e n t d e p e n d e n c e of the r e s i s t a n c e of g e r m a n i u m f i l m s s a n d w i c h e d b e t w e e n two s u p e r c o n d u c t o r s (Sn) o r b e t w e e n a s u p e r c o n d u c t o r (Sn) and a n o r m a l m e t a l (A1). T h e s a m p l e s w e r e prel~ared by e v a p o r a t i o n in a v a c u u m of b e t w e e n 10 - a and 10 - 6 m m Hg. The f i l m s w e r e d e p o s i t e d in the f o r m of a c r o s s to m a k e a f o u r - t e r m i n a l j u n c tion, a d i s c of g e r m a n i u m s e p a r a t i n g the m e t a l s t r i p s . The s t r i p s w e r e about 1 m m wide. The t h i c k n e s s e s of the f i l m s w e r e d e t e r m i n e d by int e r f e r e n c e m i c r o s c o p y on c o n t r o l s t r i p s , and the * This work has been supported by the Volkswagenwerk Foundation.
germanium layers investigated were between 290 A and 3000 A thick. The e v a p o r a t i o n c o n d i t i o n s s u g g e s t that the f i l m s a r e a m o r p h o u s [5]. E x p e r i m e n t s on S n - G e - S n s a m p l e s s h o w e d J o s e p h s o n t u n n e l l i n g with a l a r g e c r i t i c a l c u r r e n t . A b o v e the c r i t i c a l c u r r e n t , r e s i s t a n c e s of the o r d e r of 1 o h m w e r e g e n e r a l l y o b s e r v e d . The v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s ( i n s e t to fig. 1) s h o w e d c o n s i d e r a b l e h y s t e r e s i s , w h i c h m a y be due to h e a t i n g in the n o r m a l s t a t e . T h e c r i t i c a l c u r r e n t w a s found to be a d e c r e a s i n g f u n c t i o n of t e m p e r a t u r e a s i n d i c a t e d in fig. 1. E x p e r i m e n t s on S n - G e - A 1 s a m p l e s , c a r r i e d out at t e m p e r a t u r e s b e t w e e n the c r i t i c a l t e m p e r a t u r e s of Sn and A1, s h o w e d the f o l l o w i n g c h a r a c 493
Volume
33A,
i
number
i
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8
PHYSICS
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- .
.
.
.
,
|
o o o o
I00
o
or
Ic,
vI
oo° ,,,
÷. .......
"--4.
o o
-'
- "~,Ic,-;
LETTERS
28 December
to t h e r e s i s t a n c e o b s e r v e d a b o v e Tc(Sn); w h e r e a s t h e r e s i s t a n c e at low c u r r e n t s f a l l s a s t h e t e m p e r a t u r e f a l l s in a m a n n e r s i m i l a r to t h a t w h i c h we f o u n d [1] f o r C l a r k e [2] j u n c t i o n s . T h e c u r r e n t it is s u b s t a n t i a l l y t e m p e r a t u r e - i n d e p e n d e n t b e l o w 0.7 Tc(Sn ). T h e i n t e r p r e t a t i o n of e x p e r i m e n t s on t h e S n - G e - S n s a m p l e s i s s i m i l a r to t h a t of o t h e r i n v e s t i g a t i o n s of t h e p r o x i m i t y e f f e c t [3]. T r e a t i n g t h e s a m p l e s a s J o s e p h s o n j u n c t i o n s , we c a n c o m p a r e t h e d e p e n d e n c e of t h e c r i t i c a l c u r r e n t on t e m p e r a t u r e w i t h t h e p r e d i c t i o n of A m b e g a o k a r a n d B a r a t o f f [4]: ic(T ) : { ~ (T)/2eR
]2
2_4 3D T ( KELVIN)
18
3B
4.2
Fig. 1. Temperature dependence of the inereasingc u r r e n t (o) and d e c r e a s i n g - c u r r e n t (+) c r i t i c a l c u r r e n t s , c o m p a r e d with ref. [4].
•• d~ . ,7oo X
148°K
J
/
/
187"K
2.63=1( 3,38"K $.9"P'K
/ /
7 //// 0
0
0
0
}
tanh
{ ~ (T)/2hT t
U s i n g t h e m e a s u r e d v a l u e of t h e r e s i s t a n c e R i m m e d i a t e l y a b o v e Tc(Sn), t h i s f o r m u l a g i v e s t h e c u r v e in fig. 1, w h i c h w i l l b e s e e n to l i e w i t h i n t h e h y s t e r e s i s r e g i o n at a l l t e m p e r a t u r e s . In p r i n c i p l e it s h o u l d h a v e b e e n p o s s i b l e to m e a s u r e t h e p e n e t r a t i o n d e p t h of t h e s u p e r c o n d u c t i v i t y i n t o t h e g e r m a n i u m b y c o m p a r i n g l o g i at a g i v e n temperature with the thickness. Unfortunately the e v a p o r a t i o n c o n d i t i o n s w e r e not s u f f i c i e n t l y r e p r o d u c i b l e to give c o n s i s t e n t r e s u l t s h e r e . T h e e x p e r i m e n t s on S n - G e - A 1 s a m p l e s a r e m o r e d i f f i c u l t to u n d e r s t a n d . It a p p e a r s a s if a l a y e r of s u p e r c o n d u c t i v i t y i n d u c e d i n t h e g e r m a n i u m n e x t to t h e t i n i s c a r r y i n g a s u p e r c u r r e n t which short-circuits the germanium resistance. It i s on t h e s e l i n e s t h a t o u r e a r l i e r r e s u l t s [1] w e r e i n t e r p r e t e d , h o w e v e r it i s not y e t c l e a r whether an induced superconducting layer can carry a supercurrent. These results will be discussed in more det a i l in a f u r t h e r c o m m u n i c a t i o n .
0
I (MILLIAMPERES) Fig. 2. C u r r e n t - v o l t a g e c h a r a c t e r i s t i c s for Sn-Ge-A1 s a m p l e s at various t e m p e r a t u r e s . t e r i s t i c s (fig. 2). At s m a l l c u r r e n t s t h e d i f f e r e n t i a l r e s i s t a n c e i s s m a l l . At a c e r t a i n c u r r e n t i t it i n c r e a s e s ( m o r e s h a r p l y a s t h e t e m p e r a t u r e d e c r e a s e s ) to a l a r g e r v a l u e . T h e r e i s no h y s t e r e s i s , a s i s s h o w n b y d i r e c t m e a s u r e m e n t s of the differential resistance by current modulation. T h e r e s i s t a n c e to l a r g e c u r r e n t s i s a l w a y s e q u a l
494
1970
T h e a u t h o r s a r e g r a t e f u l to C. G. K u p e r a n d A. R o n f o r m a n y d i s c u s s i o n s .
References [1] s. G. Lipson, C. G. Kuper and A. Ron, Proc. Conf. on the Science of superconductivity, Stanford (1969); Physica, to be published. [2] J. Clarke, Phil. Mag. 13 (1966) 115. [3] J. Clarke, Proc. Roy. Soc. A308 (1969) 447. [4] V. Ambegaokar and A. Baratoff, Phys. Rev. L e t t e r s 10 (1963) 104. [5] K. L. Chopra and S. K. Bahl, Phys. Rev. 1 (1970) 2545.
PHYSICS
• 0,~
0.2
, ~c
L 16
' 22
2'8
' ~c
' ~,0
Fig. 2. The dependence of the critical pump parameter ~_c versus the reflection coefficient r 2 for 72 = 0.5 (hc ~ 11.0 is the corresponding critical pump parameter for the model with distributed losses). b o u n d a r y of D - d i a g r a m s e r v e s the p a r a m e t r i c c u r v e d e r i v e d f r o m eq. (2) f o r fl = i ~ and i a q ( ~ ) = = in((2) +w (~2). T h e c o m p a r i s o n of the f o u r d i f f e r e n t p a r a m e t r i c c u r v e s C1, C2, C 3 and C(r (fig. 1) p e r m i t s to e s t a b l i s h that the p o s i t i o n of the c e n t r e of the u n s t a b l e m o d e d o m a i n , i t s d i m e n s i o n s , as w e l l a s the c r i t i c a l p u m p p a r a m e t e r ;t c d e p e n d s on the d e g r e e of the f i e l d c h a n g e (r -2) in the
INDUCED
SUPERCONDUCTIVITY
LETTERS
28 December 1970
c a v i t y . T h e r e a s o n i s that the p r o b a b i l i t y of the m u l t i - p h o t o n (in p a r t i c u l a r , f o u r - p h o t o n [4]) i n t e r a c t i o n r e s p o n s i b l e f o r the o c c u r r e n c e of the i n s t a b i l i t y i n v e s t i g a t e d is d e p e n d e n t on the f r e q u e n c y d e t u n i n g (2 of the w e a k f i e l d f r e q u e n c i e s (~2o ± ~ ) f r o m the s t r o n g f i e l d f r e q u e n c y P-O and on i t s i n t e n s i t y E 2. The r e l i e f E 2 ( z ) p r o d u c e s the i n h o m o g e n e o u s b r o a d e n i n g of the r e s p o n s e at the f r e q u e n c y of the w e a k f i e l d w h i c h , in the long run, l e a d s to i n c r e a s i n g >,c a s r 2 ~ 0 ( s e e fig. 2). T h e a u t h o r e x p r e s s e s his thanks to P r o f e s s o r V. I. T a l a n o v f o r his v a l u a b l e r e m a r k s and s t e a d y i n t e r e s t for the p a p e r and a l s o P r o f e s s o r s V. I. B e s p a l o v and Ya. I. Khanin f o r u s e f u l d i s c u s s i o n .
References [1] H. Risken and K. Nummedai, Phys. Letters 26A (1968) 275. [2] N. D. Milovsky, Izv. VUZov Radiofiz. 13 {1970). [3] N.D. Milovsky, Izv. VUZov Radiofiz. 7 0964) 1095. [4] V. M. Arutyunyan, E.G. Kanetsan and V. O. Chaltykyan, J E T P 59(1970) 195.
IN
GERMANIUM
FILMS
*
S. G. LIPSON and M. M. S T U P E L Department of P h y s i c s , Technion - I s r a e l Institute of Technology, Haifa, Israel Received 25 October 1970
The voltage-current characteristics of films of Ge, sandwiched between Sn and Sn, and sandwiched between Sn and A1, have been measured at helium temperatures.
In a n u m b e r of e x p e r i m e n t s at h e l i u m t e m p e r a t u r e s we h a v e i n v e s t i g a t e d the t e m p e r a t u r e and c u r r e n t d e p e n d e n c e of the r e s i s t a n c e of g e r m a n i u m f i l m s s a n d w i c h e d b e t w e e n two s u p e r c o n d u c t o r s (Sn) o r b e t w e e n a s u p e r c o n d u c t o r (Sn) and a n o r m a l m e t a l (A1). T h e s a m p l e s w e r e prel~ared by e v a p o r a t i o n in a v a c u u m of b e t w e e n 10 - a and 10 - 6 m m Hg. The f i l m s w e r e d e p o s i t e d in the f o r m of a c r o s s to m a k e a f o u r - t e r m i n a l j u n c tion, a d i s c of g e r m a n i u m s e p a r a t i n g the m e t a l s t r i p s . The s t r i p s w e r e about 1 m m wide. The t h i c k n e s s e s of the f i l m s w e r e d e t e r m i n e d by int e r f e r e n c e m i c r o s c o p y on c o n t r o l s t r i p s , and the * This work has been supported by the Volkswagenwerk Foundation.
germanium layers investigated were between 290 A and 3000 A thick. The e v a p o r a t i o n c o n d i t i o n s s u g g e s t that the f i l m s a r e a m o r p h o u s [5]. E x p e r i m e n t s on S n - G e - S n s a m p l e s s h o w e d J o s e p h s o n t u n n e l l i n g with a l a r g e c r i t i c a l c u r r e n t . A b o v e the c r i t i c a l c u r r e n t , r e s i s t a n c e s of the o r d e r of 1 o h m w e r e g e n e r a l l y o b s e r v e d . The v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s ( i n s e t to fig. 1) s h o w e d c o n s i d e r a b l e h y s t e r e s i s , w h i c h m a y be due to h e a t i n g in the n o r m a l s t a t e . T h e c r i t i c a l c u r r e n t w a s found to be a d e c r e a s i n g f u n c t i o n of t e m p e r a t u r e a s i n d i c a t e d in fig. 1. E x p e r i m e n t s on S n - G e - A 1 s a m p l e s , c a r r i e d out at t e m p e r a t u r e s b e t w e e n the c r i t i c a l t e m p e r a t u r e s of Sn and A1, s h o w e d the f o l l o w i n g c h a r a c 493
Volume
33A,
i
number
i
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.
.
8
PHYSICS
.
,
,
,
- .
.
.
.
,
|
o o o o
I00
o
or
Ic,
vI
oo° ,,,
÷. .......
"--4.
o o
-'
- "~,Ic,-;
LETTERS
28 December
to t h e r e s i s t a n c e o b s e r v e d a b o v e Tc(Sn); w h e r e a s t h e r e s i s t a n c e at low c u r r e n t s f a l l s a s t h e t e m p e r a t u r e f a l l s in a m a n n e r s i m i l a r to t h a t w h i c h we f o u n d [1] f o r C l a r k e [2] j u n c t i o n s . T h e c u r r e n t it is s u b s t a n t i a l l y t e m p e r a t u r e - i n d e p e n d e n t b e l o w 0.7 Tc(Sn ). T h e i n t e r p r e t a t i o n of e x p e r i m e n t s on t h e S n - G e - S n s a m p l e s i s s i m i l a r to t h a t of o t h e r i n v e s t i g a t i o n s of t h e p r o x i m i t y e f f e c t [3]. T r e a t i n g t h e s a m p l e s a s J o s e p h s o n j u n c t i o n s , we c a n c o m p a r e t h e d e p e n d e n c e of t h e c r i t i c a l c u r r e n t on t e m p e r a t u r e w i t h t h e p r e d i c t i o n of A m b e g a o k a r a n d B a r a t o f f [4]: ic(T ) : { ~ (T)/2eR
]2
2_4 3D T ( KELVIN)
18
3B
4.2
Fig. 1. Temperature dependence of the inereasingc u r r e n t (o) and d e c r e a s i n g - c u r r e n t (+) c r i t i c a l c u r r e n t s , c o m p a r e d with ref. [4].
•• d~ . ,7oo X
148°K
J
/
/
187"K
2.63=1( 3,38"K $.9"P'K
/ /
7 //// 0
0
0
0
}
tanh
{ ~ (T)/2hT t
U s i n g t h e m e a s u r e d v a l u e of t h e r e s i s t a n c e R i m m e d i a t e l y a b o v e Tc(Sn), t h i s f o r m u l a g i v e s t h e c u r v e in fig. 1, w h i c h w i l l b e s e e n to l i e w i t h i n t h e h y s t e r e s i s r e g i o n at a l l t e m p e r a t u r e s . In p r i n c i p l e it s h o u l d h a v e b e e n p o s s i b l e to m e a s u r e t h e p e n e t r a t i o n d e p t h of t h e s u p e r c o n d u c t i v i t y i n t o t h e g e r m a n i u m b y c o m p a r i n g l o g i at a g i v e n temperature with the thickness. Unfortunately the e v a p o r a t i o n c o n d i t i o n s w e r e not s u f f i c i e n t l y r e p r o d u c i b l e to give c o n s i s t e n t r e s u l t s h e r e . T h e e x p e r i m e n t s on S n - G e - A 1 s a m p l e s a r e m o r e d i f f i c u l t to u n d e r s t a n d . It a p p e a r s a s if a l a y e r of s u p e r c o n d u c t i v i t y i n d u c e d i n t h e g e r m a n i u m n e x t to t h e t i n i s c a r r y i n g a s u p e r c u r r e n t which short-circuits the germanium resistance. It i s on t h e s e l i n e s t h a t o u r e a r l i e r r e s u l t s [1] w e r e i n t e r p r e t e d , h o w e v e r it i s not y e t c l e a r whether an induced superconducting layer can carry a supercurrent. These results will be discussed in more det a i l in a f u r t h e r c o m m u n i c a t i o n .
0
I (MILLIAMPERES) Fig. 2. C u r r e n t - v o l t a g e c h a r a c t e r i s t i c s for Sn-Ge-A1 s a m p l e s at various t e m p e r a t u r e s . t e r i s t i c s (fig. 2). At s m a l l c u r r e n t s t h e d i f f e r e n t i a l r e s i s t a n c e i s s m a l l . At a c e r t a i n c u r r e n t i t it i n c r e a s e s ( m o r e s h a r p l y a s t h e t e m p e r a t u r e d e c r e a s e s ) to a l a r g e r v a l u e . T h e r e i s no h y s t e r e s i s , a s i s s h o w n b y d i r e c t m e a s u r e m e n t s of the differential resistance by current modulation. T h e r e s i s t a n c e to l a r g e c u r r e n t s i s a l w a y s e q u a l
494
1970
T h e a u t h o r s a r e g r a t e f u l to C. G. K u p e r a n d A. R o n f o r m a n y d i s c u s s i o n s .
References [1] s. G. Lipson, C. G. Kuper and A. Ron, Proc. Conf. on the Science of superconductivity, Stanford (1969); Physica, to be published. [2] J. Clarke, Phil. Mag. 13 (1966) 115. [3] J. Clarke, Proc. Roy. Soc. A308 (1969) 447. [4] V. Ambegaokar and A. Baratoff, Phys. Rev. L e t t e r s 10 (1963) 104. [5] K. L. Chopra and S. K. Bahl, Phys. Rev. 1 (1970) 2545.