HAL Id: jpa-00217698
https://hal.archives-ouvertes.fr/jpa-00217698
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.
PHASE TRANSITION BETWEEN INCOHERENT
AND COHERENT SUPERCONDUCTING STATES IN
GRANULAR NbN FILMS
D. Gubser, S. Wolf
To cite this version:
JOURNAL DE PHYSIQUE
ColIoque C6, supplkment au no
8, Tome 39, aozit 1978, page
(-6-579
PHASE TRANSITION BETWEEN INCOHERENT AND COHERENT SUPERCONDUCTING STATES I N GRANULAR NbN
F I
LMSD . U . Gubser and S.A. Wolf.
NavaZ Research Laboratory Washington,
DC 20375, USA.R6sumC.- Des mesures de r d s i s t a n c e e n g o n c t i o n de l a t e m p Q r a t u r e e t d e s c a r a c t b r i s t i q u e s c o u r a n t - t e n s i o n d'un f i l m NbN u l t r a - m i n c e (30 A) m o n t r e n t l ' e x i s t e n c e d ' u n e t r a n s i t i o n d e p h a s e 1 5 . 4 K e n t r e un Q t a t s u p r a c o n d u c t e u r i n c o h e r e n t e t un Q t a t s u p r a c o n d u c t e u r c o h b r e n t . A b s t r a c t . - R e s i s t a n c e v s t e m p e r a t u r e and v o l t a g e v s c u r r e n t measurements on an u l t r a t h i n (30
i)
NbN f i l m r e v e a l t h e p r e s e n c e of a phase t r a n s i t i o n a t 5.4 K from a s u p e r c o n d u c t i n g b u t p h a s e i n - c o h e r e n t s t a t e t o a phase c o h e r e n t s u p e r c o n d u c t i n g s t a t e . I n t h e p a s t s e v e r a l y e a r s much a t t e n t i o n h a s b e e n f o c u s e d on t h e s u p e r c o n d u c t i n g p r o p e r t i e s of g r a n u l a r f i l m s . R e c e n t l y , u l t r a t h i n g r a n u l a r NbN f i l m s were found t o p o s s e s s unique s u p e r c o n d u c t i n g p r o p e r t i e s which i n c l u d e d two d i s t i n c t t r a n s i t i o nt e m p e r a t u r e s / I / . The h i g h e r t r a n s i t i o n t e m p e r a t u r e , TcG, i s t h e t e m p e r a t u r e a t which i n d i v i d u a l g r a i n s of NbN become f u l l y s u p e r c o n d u c t i n g w h i l e t h e lower t r a n s i t i o n t e m p e r a t u r e , Tcj, i s t h e t e m p e r a t u r e a t which a l l g r a i n s a r e c o h e r e n t l y coupled t o one ano- t h e r v i a J o s e p h s o n t u n n e l i n g . P r e v i o u s i n v e s t i g a t i o n s f o c u s e d on s u p e r c o n d u c t i n g p r o p e r t i e s i n t h e tempe- r a t u r e r e g i m e s above T and below Tcj. I n t h i s pa-
cG
p e r , a t t e n t i o n i s d i r e c t e a p r i m a r i l y t o t h e u n i q u e t e m p e r a t u r e r e g i o n between 'TcG and T where t h e
c j
NbN g r a i n s a r e i n c o h e r e n t l y c o u p l e d t o one a n o t h e r . The sample was p r e p a r e d from a 330 t h i c k NbN r f r e a c t i v e l y s p u t t e r e d f i l m which was subsequen- t l y t h i n n e d by a n o d i z a t i o n t o n o m i n a l l y 30 / 2 / . Both ends of t h e sample were p r o t e c t e d a g a i n s t ano- d i z a t i o n s o t h a t e l e c t r i c a l c o n n e c t i o n s c o u l d be s o l - d e r e d t o t h e f i l m / I / . The f i l m was mounted i n s i d e a v a r i a b l e t e m p e r a t u r e c r y o s t a t and f o u r t e r m i n a l r e - s i s t a n c e and c u r r e n t - v o l t a g e (I-V) measurements were o b t a i n e d a s a f u n c t i o n of t e m p e r a t u r e .
F i g u r e 1 shows t h e r e s i s t a n c e of t h e f i l m a s a f u n c t i o n o f t e m p e r a t u r e . I n s e r t A i l l u s t r a t e s f l u c - t u a t i o n p a r a c o n d u c t i v i t y above TcG. The paraconduc- t i v i t y , o b t a i n e d from t h e d i f f e r e n c e between t h e 13 t e s l a d a t a and t h e z e r o t e s l a d a t a , i s b o t h q u a l i t a - t i v e l y a n d q u a n t i t a t i v e l y c h a r a c t e r i s t i c o f z e r o dimen- s i o n a l s u p e r c o n d u c t i n g f l u c t u a t i o n s . Below TcG t h e g r a i n s of NbN a r e f u l l y s u p e r c o n d u c t i n g and weakly c o u p l e d t o one a n o t h e r s i n c e t h e remaining r e s i s t a n c e i s w e l l below t h e e s t i m a t e d r e s i s t a n c e of i n t e r g r a - n u l a r m a t e r i a l s e p a r a t i n g t h e g r a i n s . F i g . 1 : R e s i s t a n c e v s t e m p e r a t u r e f o r nominal 30 A NbN g r a n u l a r f i l m . R e s i s t a n c e measured i n z e r o ma- g n e t i c f i e l d , H = 0 , e x c e p t a s i n d i c a t e d i n i n s e r t A. I n t h i s r e g i o n t h e r e s i s t a n c e i s a f u n c t i o n of c u r - r e n t and t e m p e r a t u r e . L i m i t i n g v a l u e s of r e s i s t a n c e a t z e r o c u r r e n t a r e due t o p h a s e i n c o h e r e n t tunne- l i n g c u r r e n t s between t h e g r a i n s and a r e shown i n i n s e r t B of f i g u r e 1 . The second t r a n s i t i o n a t T
c j i s c l e a r l y o b s e r v e d i n t h i s p l o t . Below T ( 5 . 4 f
c
i
0 . 2 K) t h e sample behaves l i k e a s i n g l e , v e r y low c r i t i c a l c u r r e n t J o s e p h s o n j u n c t i o n i n d i c a t i n g a t o t a l l y phase c o h e r e n t s t a t e / I / . F i g u r e 2 shows t h e I-V c u r v e s i n t h e r e g i o n around Tcj. Below T.
t h e r e i s a a n e x t e n d e d r e g i o n C J of z e r o s l o p e i n d i c a t i n g t h e p h a s e c o h e r e n t regime. A tT
t h e r e g i o n o f z e r o s l o p e h a s s h r u n k t o a c j p o i n t a t t h e o r i g i n . The I-V c h a r a c t e r i s t i c s a t T c j a r e a c c u r a t e l y d e s c r i b e d b y a one term power law e q u a t i o n ( I i n PA and V i n pV)Above T t h e v o l t a g e i s c u r r e n t dependent and pos- c j s e s s e s a f i n i t e s l o p e a t I = 0 c h a r a c t e r i z e d by the r e s i s t a n c e v a l u e s shown i n f i g u r e 1B. Fig. 2 : Current-Voltage c h a r a c t e r i s t i c s n e a r Tcj. The l i m i t i n g v o l t a g e ( r e s i s t a n c e ) a s I + 0 i s accu-
r a t e l y d e s c r i b e d by a n o t h e r one term power law equa- t i o n
V = 6 I AT)^'^ A T = T - T > O
c j (2)
I + O
The v o l t a g e dependence a t any T and I above T c j
can, i n f a c t , be completely d e s c r i b e d i n a manner suggested t o us by Pr. Y. Imry which i s based on s c a l i n g laws of c r i t i c a l phenomena
where a i s a c o n s t a n t , x and h a r e c r i t i c a l expo- n e n t s , and
x
i s a f u n c t i o n w i t h s p e c i f i c l i m i t i n g v a l u e s . As I + 0,x
becomes p r o p o r t i o n a l t o@)'
where 1.1 i s a n o t h e r c r i t i c a l exponent ; and a s AT -+0,
x
= I . From e q s . ( I ) and ( 2 ) , which r e p r e s e n t f i t s t o experimental d a t a , t h e c r i t i c a l exponents x, A , and p a r e determined t o be 3.85 k .5, 1.14 t.3, and 2 . 5 f .5 r e s p e c t i v e l y .
Using t h e s e c r i t i c a l exponents, t h e complete f u n c t i o n can be g e n e r a t e d from t h e I-V curves and i s shown i n f i g u r e 3. The p o i n t s r e p r e s e n t v a l u e s obtained from v o l t a g e measurements taken a t v a r i o u s temperatures and c u r r e n t v a l u e s covering the e n t i r e range of d a t a . A l l measured I-V curves a r e thus ac- c u r a t e l y d e s c r i b e d by e q u a t i o n (3) using t h e graphi- c a l l y shown f u n c t i o n .
t o b e t t e r than 0.2 K due t o extreme s e n s i t i v i t y of the curves t o
RF
i n t e r f e r e n c e . AT Fig. 3 : Universal s c a l i n g f u n c t i o nX
v s-.
,
1 . 1 4,
AT = 0.15 K;A ,
AT = 0.31 K;m,
AT = 6.51K;
V,
AT = 0.61,
.
;
K
AT = 0.Exponents may a l s o be dependent on t h e magnitude of i n t e r g r a n u l a r coupling. F u t u r e e f f o r t s w i l l a d d r e s s t h e s e problem a r e a s .
In conclusion, t h e unique c h a r a c t e r i s t i c s of g r a n u l a r NbN u l t r a t h i n f i l m s have f o r t h e f i r s t time allowed the unambiguous o b s e r v a t i o n of t h e t r a n s i t i o n from a phase i n c o h e r e n t superconducting s t a t e t o a phase c o h e r e n t s t a t e . The I - V c h a r a c t e - r i s t i c s near t h i s t r a n s i t i o n a r e d e s c r i b e d by a u n i v e r s a l s c a l i n g f u n c t i o n of AT and I w i t h appro- p r i a t e exponents.
References
/ I / Wolf, S . and Lowrey, W.H., Phys. Rev. L e t t .
