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MOBILITIES OF IONS IN NORMAL AND SUPERFLUID 3He
Ydm-Group
To cite this version:
Ydm-Group. MOBILITIES OF IONS IN NORMAL AND SUPERFLUID 3He. Journal de Physique
Colloques, 1978, 39 (C6), pp.C6-1290-C6-1294. �10.1051/jphyscol:19786560�. �jpa-00218050�
I O U R N A L D E PHYSIQUE Colloque C6, supplktnent au nu 8 , Tome 39, aoCt 1978, page
C6-
1290M O B I L I T I E S O F I O N S I N NORMAL AND S U P E R F L U I D 3 ~ e
Lou T e m p e r a t u r e L a b o r a t o r y , H e l s i n k i , U n i v e r s i t y of l'echnoZogy, SF-02150 Espoo 35, F i n Land
RQsum6.- Or1 p a s s e e n r e v u e d e s e x p g r i e n c e s r g c e n t e s d e mouvements d ' i o n s d a n s l e s p h a s e s n o r m a l e s e t s u p e r f l u i d r d e 31ie. A p a r t i r d e s d i f f g r e n t e s m o b i l i t e s e n champ n u 1 d e s i o n s p o s i t i f s e t n d g a t i f s on o b t i e n t d e s i n f o r m a t i o n s s u r l e s mgcanismes d e d i f f u s i o n d e s q u a s i - p a r t i c u l e s i o n i q u e s . Dans l e s p h a s e s s u p e r f l u i d e s , l a d i f f u s i o n r g d u i t e c o n d u i t
B
u n e m o b i l i t d r a p i d e m e n t c r o i s s a n t e , q u e l ' o n trou- v e a n i s o t r o p e d a n s l a p h a s e A . Des g l i s s e m e n t s non l i n d a i r e s d e v i t e s s e d d m o n t r e n t l ' e x i s t e n c e d e v i t e s s e s c r i t i q u e s d a n s t o u t e s l e s p h a s e s . Dans c e s p h a s e s , o n t r o u v e q u e l e s i o n s b r i s e n t l e s p a i - r e s d e Cooper quand i l s d 6 p a s s e n t l a v i t e s s e c r i t i q u e d e Landau. On compare l e s r d s u l t a t s expgrimcn- t a u x a u x t h d o r i e s e x i s t a n t e s .A b s t r a c t . - R e c e n t e x p e r i m e n t s on i o n m o t i o n i n low t e m p e r a t u r e n o r m a l and s u p e r f l u i d 3 ~ e a r e r e v i e - wed. From t h e d i f f e r e n t z e r o - f i e l d m o b i l i t i e s of p o s i t i v e and n e g a t i v e i o n s i n f o r m a t i o n a b o u t t h e i o n - q u a s i p a r t i c l e s c a t t e r i n g mechanisms c a n b e o b t a i n e d . I n t h e s u p e r f l u i d p h a s e s r e d u c e d s c a t t e r i n g l e a d s t o a r a p i d l y i n c r e a s i n g m o b i l i t y , which i s found t o be a n i s o t r o p i c i n t h e A p h a s e . N o n - l i n e a r d r i f t v e l o c i t i e s d e m o n s t r a t e t h e e x i s t e n c e of c r i t i c a l v e l o c i t i e s i n a l l p h a s e s . I n b o t h s u p e r f l u i d p h a s e s t h e i o n s a r e f o u n d t o b r e a k Cooper p a i r s when t h e Landau c r i t i c a l v e l o c i t y i s e x c e e d e d . The e x p e r i m e n t a l d a t a a r e compared w i t h a v a i l a b l e t h e o r i e s .
I . INTRODUCTION.- E x p e r i m e n t s o n i o n m o t i o n i n su- p e r f l u i d 4 ~ e h a v e r e v e a l e d a g r e a t d e a l a b o u t t h e e x c i t a t i o n s p e c t r u m and t h e hydrodynamic s t r u c t u r e s o f t h e s u p e r f l u i d s u c h a s q u a n t i z e d v o r t i c e s . I t was t h e r e f o r e q u i t e o b v i o u s t h a t t h e s e e x p e r i m e n t s should be e x t e n d e d t o t h e newiy f o u n d s u p e r f l u i d p h a s e s of
?'~e. The r e d u c t i o n o f t h e q u a s i p a r t i c l e d e n s i t y be- low T was t h o u g h t t o g i v e r i s e t o a r a p i d l y i n c r e a - s i n g m o b i l i t y w i t h d e c r e a s i n g T/T
.
F u r t h e r m o r e s p e c u l a t i o n s c o u l d made a b o u t t h e e x i s t e n c e o f a Landau c r i t i c a l i o n v e l o c i t y a t w h i c h b r e a k i n g o f Cooper p a i r s by t h e moving i o n s h o u l d r e s u l t i n a s t r o n g l y i n c r e a s e d v i s c o u s d r a g on t h e i o n . I n t h e A p h a s e , f i n a l l y , a n a n i s o t r o p i c m o b i l i t y was expec-t e d t o be f o u n d .
I n v i e w o f t h e s e e x c i t i n g a s p e c t s o f i o n ex- p e r i m e n t s i n t h e s u p e r f l u i d A and B p h a s e s i t was q u i t e c l e a r t h a t a t h o r o u g h u n d e r s t a n d i n g o f t h e i n -
w e r e o b t a i n e d f o r n e g a t i v e i o n s ( e l e c t r o n b u b b l e s ) / 2 , 3 / compared t o t h o s e f o r t h e s m a l l e r and l i g h t e r p o s i t i v e s p e c i e s 1 4 1 , i n d i c a t i n g t h a t t h e s c a t t e r i n g mechanism b e t w e e n t h e q u a s i p a r t i c l e s and t h e i o n s d e p e n d s o n t h e s i z e a n d / o r t h e e f f e c t i v e mass o f t h e i o n s . I n a d d i t i o n , t h e l i n e a r r e l a t i o n s h i p b e t w e e n t h e d r i f t b e l o c i t y v and t h e a p p l i e d e l e c t r i c f i e l d E ( f r o m w h i c h t h e z e r o - f i e l d m o b i l i t y
u
= v/E h a s to b e d e t e r m i n e d ) was found t o b r e a k down a c e r t a i n d r i f t v e l o c i t i e s a b o v e w h i c h v would i n c r e a s e more s l o w l y w i t h i n c r e a s i n g E . C a r e was t a k e n t o make s u r e t h a t v was m e a s u r e d i n t h e l i n e a r r e g i m e . T h i s p r o b l e m was p a r t i c u l a r l y s e r i o u s a t low t e m p e r a t u r e s w h e r e t h e m o b i l i t i e s w e r e h i g h and h e n c e r a t h e r s m a l l e l e c t r i c f i e l d s had t o b e u s e d . T h e n o n - l i n e a r r e g i m e was a l s o s t u d i e d i n a l l p h a s e s .2. NORMAL PHASE RESULTS.- t e r a c t i o n b e t w e e n t h e i o n and t h e q u a s i p a r t i c l e s i n
2 . 1 . N e g a t i v e I o n s . - We h a v e found t h a t t h e n e g a t i - t h e n o r m a l p h a s e was r e q u i r e d a s a b a s i s f o r a quan-
v e i o n m o b i l i t y
u
i s t e m p e r a t u r e i n d e p e n d e n t down t i t a t i v e i n t e r p r e t a t i o n o f t h e s u p e r f l u i d m o b i l i -t o t h e s u p e r f l u i d t r a n s i t i o n t e m p e r a t u r e Tc /2,3/.
t i e s . T h e r e f o r e , a l s o t h e n o r m a l p h a s e (N) b e l o w
T h i s ~ l a t e a u was o b s e r v e d e a r l i e r b e t w e e n 100 mK 20 mK was i n v e s t i g a t e d f o r t h e f i r s t t i m e / I / .
and 17 mK / 5 / and c o u l d b e u n d e r s t o o d i n t e r m s of I n a l l p h a s e s (N,A,B) q u i t e d i f f e r e n t r e s u l t s
e l a s t i c q u a s i p a r t i c l e s c a t t e r i n g o f t h e i o n s l e a d i n g
+ The t~yDM-Groupt~ was t h e 1976-77 n u c l e a r demagneti- t o t h e s i m p l e e x p r e s s i o n
u
= e / o n p F w h e r e i s t h e z a t i o n g r o u p of t h e Low T e m p e r a t u r e L a b o r a t o r y and t r a n s p o r t c r o s s s e c t i o n , n t h e 3 ~ e p a r t i c l e d e n s i t y c o n s i s t e d o f t h e a u t h o r s of r e f e r e n c e s 2 t o 4 . Thep r e s e n t m a n u s c r i p t was p r e p a r e d by Dr. W. Schoepe, and pF t h e F e r m i momentum. O r i g i n a l l y , a t l o w e r tem- F a c h b e r e i c h P h y s i k d e r U n i v e r s i t 5 . t R e g e n s b u r g , p e r a t u r e s a T - ~ b e h a v i o u r was e x p e c t e d when t h e r e - D-8400 R e g e n s b u r g , F.R.G.
c o i l e n e r g y o f t h e i o n r e q u i r e s t h e i n e l a s t i c s c a t -
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786560
t e r e d q u a s i p a r t i c l e t o f i n d a n unoccupied s t a t e . Ho- wever, J o s e p h s o n and Lekner / 6 / had p o i n t e d o u t t h a t
t h e s c a t t e r i n g w i l l c o n t i n u e t o be e l a s t i c and hence t h e m o b i l i t y w i l l r e m a i n c o n s t a n t down t o v e r y low t e m p e r a t u r e . O b v i o u s l y , t h e s u p e r f l u i d t r a n s h t i o n oc- c u r s b e f o r e t h e r e c o i l mechanism makes t h e normal f l u i d i o n m o b i l i t y t e m p e r a t u r e d e p e n d e n t .
The t e m p e r a t u r e i n d e p e n d e n t p l a t e a u was ob- s e r v e d f o r a l l p r e s s u r e s between 0 and 28 b a r . I t s a b s o l u t e v a l u e i n c r e a s e d from 1 x cm2/vs a t 0 b a r t o 2.4 x lom2 cm2/vs a t 28 b a r . The i n c r e a s e i s d u e t o t h e s h r i n k i n g s i z e o f t h e b u b b l e i n which t h e e l e c t r o n i s l o c a l i z e d . Assuming a g e o m e t r i c a l s c a t t e r i n g c r o s s s e c t i o n o = n ~ t h e b u b b l e r a d i u s ~ , R a t d i f f e r e n t p r e s s u r e s can b e d e t e r m i n e d from t h e measured m o b i l i t y . The r e s u l t i s i n v e r y good a g r e - ement w i t h t h e s i m p l e b u b b l e model. The r a d i u s shrinks from 20 a t 0 b a r t o a b o u t I I a t 28 b a r . F e t t e r and ~ u r k i j z r v i 171 have e x t e n d e d t h e Josephson-Lekner f o r m a l i s m t o f i n i t e v e l o c i t i e s and have c a l c u l a t e d
t h e d e v i a t i o n s from l i n e a r i t y of v ( E ) . I n g e n e r a l n o n - l i n e a r d r i f t v e l o c i t i e s c a n be e x p t e c t e d when v
2
v = k T/pF (= 5 cm/s a t 3 mK). W i t h i n our r a n g ec B
o f e l e c t r i c f i e l d s (E
2
400 V/cm) t h e n o n - l i n e a r i t i e s were t o o s m a l l t o make a q u a n t i t a t i v e t e s t of t h et h e o r y .
2 . 2 . P o s i t i v e I o n s . - Our r e s u l t s / 4 / f o r t h e normal phase p o s i t i v e i o n m o b i l i t y a t d i f f e r e n t p r e s s u r e s a r e shown i n f i g u r e 1 . The m o b i l i t y i s c o n s i d e r a b l y h i g h e r and h a s t h e o p p o s i t e p r e s s u r e dependence o f t h e n e g a t i v e i o n d a t a . T h i s i s caused by t h e d i f f e - r e n t s t r u c t u r e s o f b o t h s p e c i e s . The p o s i t i v e i o n (snowball of s o l i d helium s u r r o u n d i n g t h e c h a r g e ) i s s m a l l e r b u t grows somewhat when h y d r o s t a t i c p r e s s u r e i s a p p l i e d .
The most s t r i k i n g f e a t u r e of t h e d a t a i s t h e l o g a r i t h m i c t e m p e r a t u r e dependence below 5 0 mK down t o T t h e s l o p e b e i n g s t e e p e r f o r t h e h i g h e r p r e s -
c '
s u r e . Above 10 mK o u r d a t a a r e i n n i c e a g r e e m e n t w i t h t h o s e of Roach e t a l . 181, however a t lower tempera- t u r e s t h e i r r e s u l t s l i e below o u r s . As can be s e e n fron. f i g u r e 2 t h e d r i f t v e l o c i t y becomes n o n - l i n e a r a t r ~ t h e r s m a l l e l e c t r i c f i e l d , e . g . below 3 mK t h e z e r o - f i e l d m o b i l i t y can be d e t e r m i n e d o n l y i f E ( 30 V/cm. The u s e o f h i g h e r f i e l d s w i l l u n d e r e s - t i m a t e t h e m o b i l i t y . T h i s may b e t h e r e a s o n f o r t h e d i s c r e p a n c y wich r e f e r e n c e 181. Most r e c e n t l y Alexander e t a l . 191 have measured t h e d r i f t v e l o c i -
t y a t h i g h f i e l d s (between 90 V/cm and 2000 Vlcm).
F i g . I : P o s i t i v e i o n m o b i l i t y i n t h e normal phase f o r d i f f e r e n t p r e s s u r e s : 0.5 b a r (+), 6 b a r (O), and 28 b a r
(a).
The s o l i d l i n e shows t h e smoothed d a t a o f r e f e r e n c e / 8 /E x t r a c t i n g t h e z e r o - f i e l d m o b i l i t y from t h e i r d a t a r e q u i r e s t h e knowledge o f t h e f u n c t i o n a l dependence o f E ( v ) and hence i n t r o d u c e s c o n s i d e r a b l e u n c e r t a i n -
t y . T h e i r r e s u l t s , t h r o u g h , a r e i n f a i r agreement w i t h o u r s which were d e t e r m i n e d s t r i c t l y i n t h e li- n e a r regime.
The r a p i d d r o p o f t h e m o b i l i t y above about 60 mK was found t o be caused by s m a l l c o n c e n t r a t i o n s of 4 ~ e i m p u r i t i e s and d o e s n o t e x i s t i n v e r y pure 3 ~ e 181.
The f a c t t h a t t h e p o s i t i v e i o n m o b i l i t y i s t e m p e r a t u r e d e p e n d e n t
-
i n c o n t r a s t t o t h e n e g a t i v e i o n m o b i l i t y-
i n d i c a t e s t h a t i n e l a s t i c s c a t t e r i n g e f f e c t s a r e i m p o r t a n t . I n f a c t , t h e p o s i t i v e i o n i s l i g h t enough t o a c q u i r e a r e c o i l e n e r g y from a qua- s i p a r t i c l e which i s n o t n e g l i g i b l e compared t o kBT, r a t h e r b e i n g o f t h e same o r d e r . However, t h e i o n d o e s n o t r e c o i l a s a f r e e p a r t i c l e s i n c e t h i s would r e s u l t i n t h e avove mentioned T - ~ b e h a v i o u r ofu .
A l o g a r i t h m i c i n c r e a s e o f t h e m o b i l i t y was r e c e n t l y p r e d i c t e d by Bowley / l o / , however o t h e r d e t a i l s of t h e t h e o r y l i k e t h e s l o p e du/dRnT a s a f u n c t i o n o f p r e s s u r e do n o t seem t o be i n agreement
JOURNAL DE PHYSIQUE
w i t h . o u r d a t a : t h e r a d i u s of t h e p o s i t i v e i o n would have t o d e c r e a s e w i t h i n c r e a s i n g p r e s s u r e , i n con- t r a s t t o t h e s n o w b a l l model.
o B PHASE
' -1
0 90 0.95 1.0
T/
r,
F i g . 3 : N e g a t i v e i o n m o b i l i t y i n t h e B p h a s e . The s o l i d l i n e i s t h e t h e o r y o f r e f e r e n c e
/
1 I / , t h e dashed l i n e i s from e q u a t i o n (1)F i g . 2 : P o s i t i v e i o n d r i f t v e l o c i t y v s . e l e c t r i c f i e l d i n t h e normal phase.
+
: 1.5 mK, 0.5 b a r ; a t 6 b a r : 2 . 6 6 mK, o 5 . 1 4 mK, 0 8.42 mK ; a t 2 8 b a r : A 3.11 mK, A 5 . 7 1 mK. The i n e l a s t i c t h r e s h o l d v e l o - c i t y k T / p i s i n d i c a t e d by a r r o w s B F3. ION MOBILITY I N THE B PHASE.-
3.1. N e g a t i v e Ions.- Below T t h e m o b i l i t y was found t o i n c r e a s e r a p i d l y w i t h d e c r e a s i n g t e m p e r a t u r e . I n f i g u r e 3 t h e r a t i o o f t h e s u p e r f l u i d t o normal pha- s e m o b i l i t y p i p n i s p l o t t e d a s a f u n c t i o n o f t h e r e d u c e d t e m p e r a t u r e TITc. W i t h i n t h e e x p e r i m e n t a l r e s o l u t i o n (dominated by t h e r e s o l u t i o n of t h e p l a -
tinum LJMK thermometer) t h e r e i s no d i f f e r e n c e b e t - ween t h e 6 b a r and t h e 18 b a r d a t a though pn i n -
c r e a s e s by 5 0 %. The r a p i d i n c r e a s e l e a d s t o d e v i a - t i o n from l i n e a r i t y o f v ( E ) a t r a t h e r s m a l l e l e c - t r i c f i e l d s . T h e r e f o r e we c o u l d n o t d e t e r m i n e t h e z e r o - f i e l d m o b i l i t y f a r below Tc (we c o u l d d e t e c t t h e s i g n a l o n l y f o r E l a r g e r t h a n about 5 Vlcm).
The o b s e r v e d i n c r e a s e o f p/p i s much s t e e p e r t h a n n
t h e one we had e x p e c t e d on t h e b a s i s o f t h e d e c r e a - s i n g number o f q u a s i p a r t i c l e s . Bayms, P e t h i c k and Salomaa showed / I 1/ t h a t i n a d d i t i o n t h e t r a n s p o r t c r o s s s e c t i o n a d e c r e a s e s when t h e l i q u i d i s cooled below Tc. T h i s d e c r e a s e i s due t o t h e f a c t t h a t t h e d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n , which i s i s o -
t r o p i c i n t h e N p h a s e , i s s t r o n g l y peaked forward i n t h e s u p e r f l u i d p h a s e and forward s c a t t e r i n g pro- c e s s e s d o n o t c o n t r i b u t e t o momentum t r a n s f e r . The r e s u l t o f t h e i r c a l c u l a t i o n g i v e s good agreement w i t h t h e d a t a . The d e v i a t i o n a t lower t e m p e r a t u r e s i s p r o b a b l y c a u s e d by i n e l a s t i c e f f e c t s which were n o t i n c l u d e d i n t h e i r t h e o r y ( e . g . a t TITc = 0.9 t h e i o n i c r e c o i l e n e r g y i s no l o n g e r s m a l l compared t o t h e w i d t h kgT of t h e q u a s i p a r t i c l e e n e r g y ) . A l s o shown i n f i g u r e 3 (dashed l i n e ) i s t h e r e s u l t one would o b t a i n i f a were t h e same a s i n t h e N p h a s e :
T h i s e x p r e s s i o n which r e f l e c t s o n l y t h e d e c r e a s i n g number of q u a s i p a r t i c l e s c l e a r l y u n d e r e s t i m a t e s t h e s u p e r f l u i d m o b i l i t y .
The n e g a t i v e i o n m o b i l i t y i n t h e B phase a t 26 b a r was measured a l s o by t h e Argonne group 1121 and t h e i r d a t a a g r e e w i t h o t l r s i n t h e temperattlre r a n g e o f o v e r l a p .
3 . 2 . P o s i t i v e i o n s . - F i g u r e 4 shows o u r r e s u l t s a t 18 b a r and 28 b a r . ( N o r m a l i z i n g p t o i t s v a l u e a t T seems t o be r e a s o n a b l e i n s p i t e o f t h e t e m p e r a t u r e dependence o f p b e c a u s e t h e t e m p e r a t u r e range in f i - g u r e 4 i s so s m a l l t h a t a n e x t r a p o l a t i o n
of"^ "
i n t o t h e s u p e r f l u i d would g i v e o n l y a 4% v a r i a t i o n o f 28 b a r d a t a ) . There is a s l i g h t p r e s s u r e dependence, t h e28 b a r d a t a b e i n g above t h e 18 b a r d a t a . The most i n t e r e s t i n g f e a t u r e , t h o u g h , i s t h e much s m a l l e r r e l a t i v e i n c r e a s e of t h e p o s i t i v e i o n m o b i l i t y below Tc t h a n t h e one we found f o r n e t a t i v e i o n s / 1 3 / . For comparison, e q u a t i o n 1 which i n t h e c a s e o f n e g a t i v e i o n s i s t o o low by a f a c t o r o f a b o u t 2 i s c l e a r l y c o n s i d e r a b l y above t h e e x p e r i m e n t a l d a t a . I t seems t h a t i n e l a s t i c s c a t t e r i n g which made p t o i n c r e a s e w i t h d e c r e a s i n g t e m p e r a t u r e now p r e v e n t s t h e p o s i -
t i v e i o n m o b i l i t y i n t h e B p h a s e from growing a s f a s t a s i n t h e c a s e of e l e a s t i c s c a t t e r i n g ( i . e . n e g a t i v e i o n s ) . To d a t e , no t h e o r y i s a v a i l a b l e t o e x p l a i n q u a n t i t a t i v e l y o u r e x p e r i m e n t a l d a t a .
18 bar
1 0 0
LAL
85 0 90 0 95 10T/ T,
F i g . 4 : P o s i t i v e i o n m o b i l i t y i n t h e B p h a s e . The s o l i d l i n e i s from e q u a t i o n 1
4. ANISOTROPIC MOBILITY I N THE A PHASE.- I n t h e A phase t h e i o n m o b i l i t y i s a n i s o t r o p i c b e c a u s e t h e s i z e of t h e e n e r g y gap i n t h e d i r e c t i o n o f t h e d r i f t v e l o c i t y
;
depends upon t h e a n g l e between v and t h e 3-+ E v e c t o r : i o n s moving p a r a l l e l t o
d
e n c o u n t e r more -+q u a s i p a r t i c l e s t h a n p e r p e n d i c u l a r t o
d .
S i n c e Q i s o r i e n t e d i n a p l a n e p e r p e n d i c u l a r t o t h e e x t e r n a l m a g n e t i c f i e l d B we e x p e c t t h e m o b i l i t y t o be l a r -+ + + +
g a r when B//E t h a n i r i t h e c a s e where BLE. It s h o u l d b e n o t e d t h a t o n l y f o r
$//$
h a s t h e d r i f t v e l o c i t y a w e l l d e f i n e d a n g l e w i t h r e s p e c t t o + E ( 9 0 ° ) , whe-+ +
r e a s f o r BLE a l l a n g l e s a r e p o s s i b l e b e c a u s e o n l y t h e p l a n e c f t h e + 2. v e c t o r i s f i x e d . C o n s e q u e n t l y , o n l y a n a v e r a g e d m o b i l i t y c a n be d e t e r a i n e d f o r
2 L ~
-+which i n a d d i t i o n might be s e n s i t i v e t o o t h e r o r d e - r i n g mechanism which g i v e r i s e t o t e x t u r e s .
The a n i s o t r o p y i s c l e a r l y v i s i b l e i n t h e p o s i t i v e i o n d a t a of f i g u r e 5. p(B//E) i s l a r g e r than
p(BLE) and w i t h i n o u r r e s o l u t i o n merges smoothly i n - t o t h e B p h a s e d a t a a t TAB. The jump of u ( B ~ E ) a t TAB i s somewhat l a r g e r t h a n t h e one o b s e r v e d by t h e Argonne g r o u p /12/ b u t t h i s might be due t o t h e abo- v e mentioned t e x t u r a l e f f e c t s . The s m a l l d i s c o n t i - n u i t y of p ( B / / E ) a t TAB which was r e p o r t e d i n r e f e - r e n c e / 12/ was n o t s e e n by u s .
F i g . 5 : P o s i t i v e i o n m o b i l i t y i n t h e s u p e r f l u i d p h a s e s a t 28 b a r f o r two o r i e n t a t i o n s of t h e m a g n e t i c f i e l d
For n e g a t i v e i o n s a simil;zr a n i s o t r o p y i s o b s e r v e d w i t h v(B//E) b e i n g l a r g e r t h a n II (BlE) and merging smoothly i n t o t h e B p h a s e c u r v e / 3 , 1 2 / .
We c a n c o n c l u d e t h a t f o r b o t h t y p e s of c h a r - ge c a r r i e r s t h e m o b i l i t y i s l a r g e r when t h e i o n mo- v e s p e r p e n d i c u l a r l y t o -+ E, i . e . i n t h e d i r e c t i o n of t h e maximal e n e r g y g a p , t h a n i n t h e d i r e c t i o n of Q + where t h e gap v a n i s h e s . C a l c u l a t i o n s o f t h e m o b i l i t y
t e n s o r i n t h e A p h a s e i n v o l v e c o n s i d e r a b l e mathema- t i c a l work b u t a r e i n p r o g r e s s / 1 4 / .
5. PAIR BREAKING BY IONS.- A l l o f o u r m o b i l i t y d a t a were d e t e r m i n e d i n t h e regime where t h e d r i f t v e l o - c i t y i s p r o p o r t i o n a l t o t h e e l e c t r i c f i e l d . I n t h e s u p e r f l u i d p h a s e s we c o u l d n o t d e t e r m i n e t h e m o b i l i - t y below T/Tc % 0 . 8 b e c a u s e d e v i a t i o n s from l i n e a r i - t y o c c u r r e d a t d e c r e a s i n g l y s m a l l e l e c t r i c f i e l d s as shown i n f i g u r e 6 . As t h e t e m p e r a t u r e i s lowered the i n i t i a l s l o p e of t h e v ( E ) c u r v e s becomes s t e e p e r be- c a u s e t h e m o b i l i t y i n c r e a s e s . However, f o r v e l o c i - t i e s above % 7 cm/s v i n c r e a s e s no l o n g e r p r o p o r t i o - n a l t o E and f i n a l l y t h e s l o p e o f f u r t h e r v e l o c i t y
C6-
1294 JOURNAL DE PHYSIQUEchanges dv/dE becomes t h e same a s t h e one observed i n t h e N phase. T h j s b e h a v i o u r was found i n b o t h su- p e r f l u i d p h a s e s and f o r b o t h i o n s p e c i e s .
F i g . 6 : P o s i t i v e i o n d r i f t v e l o c i t y v s . e l e c t r i c f i e l d
i h
t h e s u p e r f l u i d p h a s e s a t 28 b a r . A ( 0 ) / p F i s Landau's c r i t i c a l v e l o c i t y f o r p a i r b r e a k i n g a t T = OA s i m p l e e x p l a n a t i o n f o r t h i s o b s e r v a t i o n can be g i v e n i n t e r n s of L a n d a u ' s c r i t i c a l v e l o c i t y . When t h e moving i o n e x c e e d s a c r i t i c a l v e l o c i t y v = AlpF i t w i l l b r e a k s u p e r f l u i d p a i r s and w i l l l o s e more momentum t h a n below v
.
Taking t h e BCS v a l u e f o r A a t z e r o t e m p e r a t u r e , v = A ( 0 ) / P F i s7 cm/s which a g r e e s w i t h t h e o b s e r v e d o n s e t of t h e n o n l i n e a r b e h a v i o u r . Thus we have e v i d e n c e f o r t h e e x i s t e n c e of a Landau c r i t i c a l v e l o c i t y f o r p a i r b r e a k i n g i n s u p e r f l u i d 3 ~ e . The s i t u a t i o n i n a n a l o - gous t o t h e Landau c r i t i c a l v e l o c i t y f o r r o t o n ex- c i t a t i o n i n s u p e r f l u i d 4 ~ e which was observed i n ion e x p e r i m e n t s e a r l i e r /
Is/.
The n o n l i n e a r v e l o c i t y regime f o r n e g a t i v e i o n s i n t h e B y h a s c h a s been s t u d i e d by F e t t e r and K u r k i j z r v i / 7 / . Though t h e i r t h e o r y l e a d s t o d i v e r - g i n g i n t e g r a l s i n t h e z e r o - v e l o c i t y l i m i t , t h e c a l - c u l a t e d c u r v e s r e s e m b l e q u a l i t a t i v e l y t h e experimen- t a l d a t a f o r h i g h v e l o c i t i e s : t h e c u r v e s bend o v e r a t v = v = A/pF and f o r v > > v c t h e d r a g f o r c e ap- p r o a c h e s t h e normal s t a t e v a l u e .
6. CONCLUSION.- The e x p e r i m e n t s on i o n m o t i o n i n s u p e r f l u i d 3 ~ e which have been performed s o f a r ha-
v e y i e l d e d i n t e r e s t i n g i r ~ f o r m a t i o n a b o u t s c a t t e r i n g p r o c e s s e s o f t h e q u a s i p a r t i c l e s and w i l l c e r t a i n l y b e extended i n t h e n e a r f u t u r e . I n p a r t i c u l a r mea- s u r e m e n t s of t h e m o b i l i t y a t lower t e m p e r a t u r e s t h a n T/T 2. 0 . 8 would b e u s e f u l . The e x p e r i m e n t a l pro- blems h e r e a r e o b v i o u s : d a t a have t o be t a k e n a t m u c h s m a l l e r e l e c t r i c f i e l d s .
Also o u r t h e o r e t i c a l u n d e r s t a n d i n g of i o n mo- t i o n i n low t e m p e r a t u r e 3 ~ e i s s t i l l r a t h e r p o o r , w i t h t h e e x e c p t i o n o f n e g a t i v e i o n s i n t h e N and B phase c l o s e t o Tc. E s p e c i a l l y i n e l a s t i c s c a t t e r i n g p r o c e s s e s which d o m i n a t e t h e m o t i o n of t h e l i g h t and s m a l l p o s i t i v e c a r r i e r w i l l have t o be s t u d i e d . And f i n a l l y we hope t h a t a t h e o r e t i c a l d e s c r i p t i o n o f t h e c o m p l e t e v(E) c u r v e s w i l l a l l o w a mapping o f t h e p r e s s u r e and t e m p e r a t u r e dependence of t h e e n e r - gy gap.
The q u e s t i o n t o what e x t e n t i o n s c a n b e used t o e x c i t e o r d e t e c t hydrodynamic s t r u c t u r e s i n s u p e r -
f l u i d 3 ~ e such a s q u a n t i z e d v o r t i c e s o r t e x t u r e s remains t o be i n v e s t i g a t e d i n t h e f u t u r e .
R e f e r e n c e s
/ I / For a r e v i e w on e a r l i e r i o n work s e e t h e a r t i c l e by F e t t e r , A . L . , i n The P h y s i c s of L i q u i d and S o l i d Helium, K.H. Bennemann and J . B . K e t t e r s o n , e d s . (Wiley, New York) 1976, pp. 242-305
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37
(1976) 51 1 / 3 / Ahonen, A . I . , Kokko, J . , P a a l a n e n , M . A . ,R i c h a r d s o n , R.C., Schoepe, W . , and Takano, Y . , Low Temp. Phys.
2
(1978) 205/ 4 / Kokko, J . , P a a l a n e n , M . A . , Schoepe, W . , and Takano, Y . . J . Low Temp. P h y s . , t o be p u b l i s h e d / 5 / Kuchnir, M . , Roach, P.R., and K e t t e r s o n , J . B . ,
Phys. Rev.
A
((1970) 262/ 6 / J o s e p h s o n , B . D . , Lekner, J . , Phys. Rev. L e t t . 3 (1969) 1 1 1
/ 7 / F e t t e r , A.L., and K u r k i j z r v i , J . , Phys. Rev.
B 15 (1977) 4272 -
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63
(1977) 273/ 9 / A l e x a n d e r , P.W., B a r b e r , C . N . , McClintock,P.V.E., and P i c k e t t , G.R., Phys. Rev. L e t t .
2
(1977) 1544/ l o / Bowley, R . M . , J . Phys.
C
((1978) 75/ 1 1 / Baym, G . , P e t h i c k , C . J . , and Salomaa, M . , Phys.
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2
(1977) 8451 1 2 1 Roach, P.D., K e t t e r s o n , J.B., and Roach, P.R., Phys. Rev. L e t t .
39
(1977) 626I 1 3 1 The same o b s e r v a t i o n was made by t h e Argonne g r o u p , r e f e r e n c e / 1 2 /
1141 Salomaa, M . , p r i v a t e c o m u n i c a t i o n
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