HYSTERESIS OF THE CRITICAL CURRENT IN NONEQUILIBRIUM SUPERCONDUCTORS

(1)

HAL Id: jpa-00217645

https://hal.archives-ouvertes.fr/jpa-00217645

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

HYSTERESIS OF THE CRITICAL CURRENT IN

NONEQUILIBRIUM SUPERCONDUCTORS

G. Dharmadurai, B.a . Ratham

To cite this version:

(2)

JOURNAL DE PHYSIQUE

_{Colloque C6, supplPment au no 8 , Tome 39, aolit}

_1978,

_{page C6-507}

i

Bhabha Atomic Research Centre, Bombay

400 085

rr Tata I n s t i t u t e o f FundamentaZ Research, Homi Bhabha Road, Bombay

400 005

Rdsum6.- On p r d s e n t e l e s r 6 s u l t a t s des i n v e s t i g a t i o n s expdrimentales d ' h y s t l r c s i s du c o u r a n t

c r i t i q u e dans l e s ponts supraconducteurs 1 e f f e t de proximitd p o r t d s h o r s d T & q u i l i b r e par

i n j e c t i o n de phonons 1 t r a v e r s une bande m s t a l l i q u e , normale e t t r a n s v e r s a l e . On examine l e

r a p p o r t des r d s u l t a t s aux thi5ories e x i s t a n t e s de supraconducteurs h o r s d T 6 q u i l i b r e .

A b s t r a c t . - The r e s u l t s of our experimental i n v e s t i g a t i o n s of t h e h y s t e r e s i s of t h e c r i t i c a l c u r r e n t i n superconducting proximity e f f e c t b r i d g e s d r i v e n i n t o nonequilibrium s t a t e s by i n - j e c t i n g phonons through t h e t r a n s v e r s e normal metal s t r i p a r e r e p o r t e d . The r e l e v a n c e of t h e r e s u l t s t o t h e e x i s t i n g t h e o r i e s of non-equilibrium superconductors i s examined.

INTRODUCTION.- Recently, t h e r e h a s been an i n c r e a - s i n g i n t e r e s t i n t h e s t u d y of t h e p r o p e r t i e s of superconductors d r i v e n i n t o nonequilibrium s t a t e s by e x t e r n a l mechanisms such a s q u a s i p a r t i c l e in- j e c t i o n , photon i n j e c t i o n and phonon i n j e c t i o n 11-3). I n t h i s paper we r e p o r t t h e r e s u l t s of our experimental s t u d y of an i n t e r e s t i n g p r o p e r t y ( v i z . t h e h y s t e r e s i s of t h e c r i t i c a l c u r r e n t ) of l o n g superconducting p r o x i m i t y - e f f e c t b r i d g e s d r i v e n i n t o nonequilibrium s t a t e s by phonon i n j e c t i o n through

t h e t r a n s v e r s e normalmetal s t r i p . I n t h e e v e n t of t h e f a i l u r e of a simple h e a t i n g model t o account f o r t h e i n c r e a s e i n t h e e x p e r i m e n t a l l y observed e f f e c t i v e b r i d g e temperature i n t h e nonequilibrium s t a t e , we f i n d t h a t one h a s t o invoke t h e P a r k e r ' s

T* model / 4 / ( a l s o known a s t h e "Modified h e a t i n g

t h e o r y of nonequilibrium superconductor's) t o e x p l a i n t h e r e s u l t s .

EXPERIMENTAL.- The s t r u c t u r e s used i n our e x p e r i -

ments a r e crossed t h i n f i l m s t r i p s of t i n and s i l -

v e r ( s e e i n s e t f i g u r e l ) prepared by s e q u e n t i a l vacuum e v a p o r a t i o n of t h e s e m a t e r i a l s onto c l e a n g l a s s s u b s t r a t e s . The t r a n s i t i o n temperature of

t h e o v e r l a y r e g i o n i s depressed r e l a t i v e t o t h e

main f i l m by t h e p r o x i m i t y - e f f e c t of t h e normal

metal on t h e superconductor / 5 / . The o v e r l a y sec-

t i o n s a r e of l e n g t h s v a r y i n g between 200 pm and

500 pm and width

=

200 pm. The t h i c k n e s s of t h e

s i l v e r and t i n s t r i p s vary between 0.1 pm and 0.3 pm. The samples a r e mounted v e r t i c a l l y i n a tResearch c a r r i e d o u t a t t h e T a t a I n s t i t u t e of

Fundamental Research.

l i q u i d helium b a t h which can be pumped down t o lower t h e temperature upto 1.6 K . A manostat i s used t o c o n t r o l t h e b a t h temperature which i s mea- s u r e d b y m o n i t o r i n g t h e vapour p r e s s u r e over t h e helium b a t h .

1

F i g . 1 : The dependence of ( 6 I ) 2 on T and I:.

The i n s e t shows t h e I-V c h a r a c t g r i s t i c s of a

t y p i c a l p r o x i m i t y - e f f e c t b r i d g e (TD 259)

e t

two

d i f f e r e n t b a t h temperatures and t h e sample geo-

me t r y .

RESULTS AND DISCUSSION.- F i g u r e 1 ( i n s e t ) shows

t h e c u r r e n t - v o l t a g e

(I-V)

c h a r a c t e r i s t i c s of a

typiCal p r o x i m i t y - e f f e c t b r i d g e (TD 259)obtained a t two d i f f e r e n t b a t h temperatures which e x h i b i t t h e g e n e r a l f e a t u r e s s i m i l a r t o t h o s e observed by p r e v i o u s workers / 5 , 6 / w i t h w e l l d e f i n e d metasta-

b l e c r i t i c a l c u r r e n t s I _{c l} and I and t h e

c 2

(3)

h y s t e r e s i s o f t h e c r i t i c a l c u r r e n t i n c r e a s i n g a s t h e t e m p e r a t u r e i s lowered. The s p e c i a l f e a t u r e observed i n o u r e x p e r i m e n t s i s t h a t when a d i r e c t c u r r e n t ( I ) i s i n j e c t e d through t h e normal-metal J s t r i p , n o n e q u i l i b r i u m q u a s i p a r t i c l e s a r e g e n e r a t e d i n t h e p r o x i m i t y - e f f e c t b r i d g e by p a i r b r e a k i n g by t h e r m a l phonons from t h i s h e a t e r s t r i p / 2 / and con- s e q u e n t l y t h e o v e r l a y r e g i o n i s weakened f u r t h e r c a u s i n g a d e c r e a s e i n t h e h y s t e r e s i s of t h e c r i t i - c a l c u r r e n t which i s r e m i n i s c e n t o f a n e f f e c t o b s e r v e d when t h e b a t h t e m p e r a t u r e i s r a i s e d . A t b a t h t e m p e r a t u r e s c l o s e t o ( b u t lower than) t h e b u l k t r a n s i t i o n t e m p e r a t u r e o f t h e pro- x i m i t y - e f f e c t b r i d g e we o b s e r v e ( s e e f i g u r e 1) t h a t t h e s q u a r e r o o t o f t h e c r i t i c a l c u r r e n t d i f f e r e n c e ( 6 1 ~ ) ' ~ ~ v a r i e s l i n e a r l y w i t h ( i ) b a t h t e m p e r a t u r e (T) f o r z e r o i n j e c t i o n c u r r e n t and ( i i ) s q u a r e o f t h e i n j e c t i o n c u r r e n t ( I ~ ) a t a f i x e d b a t h tempe- J

r a t u r e where 6 1 = I c l

-

Ic2. These o b s e r v a t i o n s

a s s u c h have no t h e o r e t i c a l e x p l a n a t i o n . I f we a s - sume t h e p r o p e r t i e s ( i n o u r c a s e , t h e h y s t e r e s i s of t h e c r i t i c a l c u r r e n t ) o f a n o n e q u i l i b r i u m su- p e r c o n d u c t o r t o b e t h e t h e r m a l e q u i l i b r i u m p r o p e r - t i e s o f a n o r d i n a r y s u p e r c o n d u c t o r a t a n e f f e c t i v e t e m p e r a t u r e 'T g r e a t e r t h a n t h e helium-bath tempe- r a t u r e , f i g u r e 1 c a n b e used t o e v a l u t e t h e e f f e c - I t i v e t e m p e r a t u r e T c o r r e s p o n d i n g t o an i n j e c t i o n c u r r e n t IJ ( s e e t a b l e I ) .

Table I . Comparison o f t h e e f f e c t i v e temperature(TZ)

- -

I

I n j e c t o r C u r r e n t

I

IJ (mA)

7

l 0

j

1

.o

i I l 1.5 ! _2.0

1

2.5 3 .O

j

3.5 I E f f e c t i v e t e m p e r a t u r e Tg (K) 1 I--- 1

:

u s i n g eq. ( 1 ) from f i g . 1 l 7 l 1

-

l l

;

2.220

:

2.220 l I I l I 2.232 v 2.235 l l

;

2.248 2.252 1 l l I 2.269 2.274 l

.

l l 1 2.295 I 2.303 l l l I 2.325 2.336 1 I To examine w h e t h e r t h e o b s e r v e d phenomena i s r e s u l t o f p u r e h e a t i n g , we u s e a s i m p l e h e a t i n g model which assumes t h a t t h e o n l y e f f e c t o f t h e

phonon i n j e c t i o n i s t o r a i s e t h e t e m p e r a t u r e w h i l e

t h e s u p e r c o n d u c t o r remains i n complete t h e r m a l

e q u i l i b r i u m a t t h e e l e v a t e d t e m p e r a t u r e (T*) d e t e r -

mined by t h e h e a t imput and t h e thermal boundary conductance between t h e t h i n f i l m and t h e s u b s t r a t e

a n d / o r t h e l i q u i d helium. The t h e r m a l conductance depends on t h e d i f f e r e n c e o f t h e f o u r t h powers of t h e f i l m and ambient t e m p e r a t u r e s 171. I n t h i s c a s e , T' i s o b t a i n e d u s i n g t h e r e l a t i o n / 4 / , 4 4 2 2

TH

-

T = ccIJ/IJO

...

( 1 ) where cc i s a d j u s t e d s o t h a t T* = Tc when I ~ / I ~ ~ = I ~ ~

and IJO i s t h e c r i t i c a l i n j e c t o r c u r r e n t which

d r i v e s normal t h e p r o x i m i t y - e f f e c t b r i d g e . The va- l u e s o f T* e s t i m a t e d u s i n g e q u a t i o n ( 1 ) a r e o b s e r - ved ( s e e t a b l e I ) t o d e v i a t e from t h o s e o b t a i n e d

from t h e e x p e r i m e n t a l d a t a (of f i g u r e I ) and a r e l e s s e r i n magnitude. T h i s s u g g e s t s t h a t t o e x p l a i n t h e observed d e v i a t i o n one h a s t o invoke t h e P a r - k e r ' s T* model / 4 / where t h e e f f e c t i v e t e m p e r a t u r e I T i s s i g n i f i c a n t l y g r e a t e r t h a n t h e i n c r e a s e d t e m p e r a t u r e r e s u l t i n g from p u r e h e a t i n g . D e f e r r i n g a d e t a i l e d a n a l y s i s of t h e expe- r i m e n t a l s i t u a t i o n and i t s c o n n e c t i o n w i t h t h e T*

model t o a d e t a i l e d p u b l i c a t i o n ,we have merely shown t h a t t h e o b s e r v e d d e v i a t i o n from a s i m p l e

h e a t i n g model i s c o n s i s t e n t w i t h t h e m o d i f i e d hea-

t i n g model / 4 / i n which t h e i n j e c t e d e n e r g y i s c o n c e n t r a t e d among t h e high-energy phonons r e s u l - t i n g i n a g r e a t e r i n c r e a s e i n t h e number o f t h e s e phonons, and hence a g r e a t e r e f f e c t i v e t e m p e r a t u r e ,

t h a n i f t h e i n j e c t e d e n e r g y i s d i s t r i b u t e d among phonons o f a l l e n e r g y .

R e f e r e n c e s

1 1

1

Langenberg, D .N., Low Temperature P h y s i c s

-

LT 14 e d i t e d by M.Krusius and M. Vuorio (North

Holland, Amsterdam, 1975) Vol.V, p . 223. / 2 / Ting-Wah Wong, Yeh, J.T.C. and Langenberg,D.N.,

Phys. Rev. L e t t . 37 (1976) 150 and IEEE T r a n s .

Mag. MAG-13 ( 1 9 7 7 r 7 4 3 .

/ 3 / I g u c h i , I.,Phys.Rev. (1977) 1954 and Phys.

L e t t . 64A (1978) 415.

-

_

/ 4 / P a r k e r , W.H. ,Phys .Rev.

B12

(1975) 3667.

1 5 1 N o t a r y s , H.A.and Mercereau,J.E.. J.Appl.Phys.

44 (1973) 1821.

-

161 Decker,S.K. and Palmer, D.W.,J.Appl. P h y s . 4 8 (1977) 2043.