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R E C E N T R E S U L T S O N C H A R G E D E N S I T Y W A V E S :
t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t a n d Z e e m a n s p l i t t i n g
o f s o l i t o n d i p o l e s
R g i s M l i n
" # % ( 0 0 % 2 3 5 " 84( @ B " # @ E 8G8 H G" I ( PGP RP 84( S ( @ G5 B I ( % I % @ X @ ` a d@ e f 5 g f i Pr s t u v
#" $ & (0 1 1 & 354 6 " 9 ( A E " $ AC H 9#9 " Q ( R#R #R S A 9 T9 U A A W WQ " ( A A Y A $ U & 9 5 Rb c e g h
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S e m i n a r i s d i v i d e d i n t w o p a r t s r e l a t e d t o e x p e r i m e n t s o n C D W s c a r r i e d o u t i n G r e n o b l e i n t h e
g r o u p o f P . M o n c e a u :
A ) R e s u l t s o b t a i n e d i n c o l l a b o r a t i o n w i t h S . D u h o t o n C D W n a n o s c a l e e x p e r i m e n t s
c a r r i e d o u t b y Y u . I . L a t y s h e v , A . A . S i n c h e n k o
B ) D i s c u s s i o n o f r e c e n t r e s u l t s o n t h e h e a t r e l a x a t i o n e x p e r i m e n t s c a r r i e d o u t b y :
J . C . L a s j a u n i a s ( G r e n o b l e ) , S . S a h l i n g ( D r e s d e n ) , G . R e m e n y i ( G r e n o -
b l e ) , K . B i l j a k o v i c ( Z a g r e b ) .
R e d : c o l l a b o r a t i o n ; B l u e : d i s c u s s i o n s
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E
E
0
1D metal
0
No gap in the
excitation
spectrum
Gapped
excitations
Ground state
1D metal + lattice distorsions
= charge density wave
Large density
Small density
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I n t r o d u c t i o n : w h a t a b o u t a S Q U I D w i t h C D W s ?
L e t ' s r s t l o o k a t a s q u i d w i t h s u p e r c o n d u c t o r s w i t h i n l o w e s t o r d e r p r o c e s s e s i n
t h e J o s e p h s o n j u n c t i o n t r a n s p a r e n c i e s :
e
e
e
e
e
e
e
ee
e
e
e
e
e
e
e
FLUX
P a i r p h a s e f a c t o r
exp
ie/h
ZA.dr ie/h
ZA.dr
= exp
2ie/h
ZA.dr
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S q u i d w i t h a C D W ?
e
e
e
e
e
e
e
e
FLUX
h
h
h
h h
h
h
h
E l e c t r o n - h o l e p h a s e f a c t o r
exp`ie/h
RA.dr + ie/h
RA.dr
= exp (0) = 1
S o m e w h a t h e u r i s t i c n a i v e p i c t u r e b e c a u s e t h e c u r r e n t - p h a s e r e l a t i o n i s d i e r e n t i n s u p e r c o n d u c -
t o r s a n d C D W s + g e o m e t r i c a l c o n s t r a i n t s .
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O K , l e t ' s l o o k a t t h e L a t y s h e v e x p e r i m e n t !
B
Direction of current flow
Columnar defects
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T o p v i e w o f t h e L a t y s h e v e x p e r i m e n t
B
Direction of current flow
Columnar defects
Nanoholes
Direction of current flow
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M o r e r e a l i s t i c p o i n t o f v i e w
B
Direction of current flow
Columnar defects
NanoholesDamaged area
Direction of current flow
L e v e l s p a c i n g Peierls o f t h e n o r m a l d a m a g e d r e g i o n b e c a u s e
N a n o h o l e d i a m e t e r C D W c o h e r e n c e l e n g t h 1 0 n m
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E x p e r i m e n t a l d a t a
L a t y s h e v , L a b o r d e , M o n c e a u , K l a u m n z e r , P R L 7 8 , 9 1 9 ( ' 9 7 )
h/2ep e r i o d i c o s c i l l a t i o n s . S o , i s i t a S Q U I D ( i e p h a s e c o h e r e n c e + c o l l e c t i v e m o t i o n ) o r
s o m e t h i n g e l s e ?
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A n y m a n i f e s t a t i o n o f a c o l l e c t i v e q u a n t u m m e c h a n i c a l g r o u n d s t a t e i n c h a r g e
d e n s i t y w a v e s ?
Q u e s t i o n 1 : A n y s i g n a t u r e o f q u a n t u m m e c h a n i c s a t v e r y l o w t e m p e r a t u r e ?
A n s w e r 1 : S p e c i c h e a t e x p e r i m e n t s , e x c i t a t i o n s o f C D W a s c l a s s i c a l , n o g e n u i n e e v i d e n c e o f
t u n n e l i n g ( e x p : L a s j a u n i a s e t a l . ) .
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A n y m a n i f e s t a t i o n o f a c o l l e c t i v e q u a n t u m m e c h a n i c a l g r o u n d s t a t e i n c h a r g e
d e n s i t y w a v e s ?
Q u e s t i o n 1 : A n y s i g n a t u r e o f q u a n t u m m e c h a n i c s a t v e r y l o w t e m p e r a t u r e ?
A n s w e r 1 : S p e c i c h e a t e x p e r i m e n t s , e x c i t a t i o n s o f C D W a s c l a s s i c a l , n o g e n u i n e e v i d e n c e o f
t u n n e l i n g ( e x p : L a s j a u n i a s e t a l . ) .
Q u e s t i o n 2 : W h a t a b o u t p r o b i n g p h a s e c o h e r e n c e i n a C D W b y t h e J o s e p h s o n e e c t i n
S - C D W - S j u n c t i o n s ? M e s o s c o p i c C D W c a n b e d e p i n n e d b y t h e J o s e p h s o n e e c t ?
A n s w e r 2 : C o n n e c t i o n w i t h c r o s s e d A n d r e e v r e e c t i o n i n N - S - N j u n c t i o n s n o J o s e p h s o n
c u r r e n t b e y o n d F t h r o u g h a C D W ( e x p o n C D W s : S i n c h e n k o a n d M o n c e a u ) , J o s e p h s o n c u r r e n t
o v e r SDW t h r o u g h a S D W .
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A n y m a n i f e s t a t i o n o f a c o l l e c t i v e q u a n t u m m e c h a n i c a l g r o u n d s t a t e i n c h a r g e
d e n s i t y w a v e s ?
Q u e s t i o n 1 : A n y s i g n a t u r e o f q u a n t u m m e c h a n i c s a t v e r y l o w t e m p e r a t u r e ?
A n s w e r 1 : S p e c i c h e a t e x p e r i m e n t s , e x c i t a t i o n s o f C D W a s c l a s s i c a l , n o g e n u i n e e v i d e n c e o f
t u n n e l i n g ( e x p : L a s j a u n i a s e t a l . ) .
Q u e s t i o n 2 : W h a t a b o u t p r o b i n g p h a s e c o h e r e n c e i n a C D W b y t h e J o s e p h s o n e e c t i n
S - C D W - S j u n c t i o n s ? M e s o s c o p i c C D W c a n b e d e p i n n e d b y t h e J o s e p h s o n e e c t ?
A n s w e r 2 : C o n n e c t i o n w i t h c r o s s e d A n d r e e v r e e c t i o n i n N - S - N j u n c t i o n s n o J o s e p h s o n
c u r r e n t b e y o n d F t h r o u g h a C D W ( e x p o n C D W s : S i n c h e n k o a n d M o n c e a u ) , J o s e p h s o n c u r r e n t
o v e r SDW t h r o u g h a S D W .
Q u e s t i o n 3 : A n y s i g n a t u r e o f t h e C D W c o n d e n s a t e i n t r a n s p o r t p r o p e r t i e s , m a y b e i n t h e
L a t y s h e v e x p e r i m e n t ? N o t a 1 D r i n g g e o m e t r y !
A n s w e r 3 : W e a k l o c a l i z a t i o n - l i k e e e c t s h/2e o s c i l l a t i o n s t h e m a g n e t o r e s i s t a n c e . C o n -
n e c t i o n w i t h n o n s t a n d a r d f e a t u r e s o f l o c a l i z a t i o n , a n d w i t h s u p e r c o n d u c t i n g h y b r i d s .
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O u t l i n e
A ) N I N a n d N S N s t r u c t u r e s b e y o n d l o w e s t o r d e r p e r t u r b a t i o n i n t h e i n t e r f a c e t r a n s p a r e n c i e s
A . 1 . N o r m a l t u n n e l j u n c t i o n s : a l r e a d y a c o l l e c t i v e c h a n n e l
A . 2 . W e a k l o c a l i z a t i o n - l i k e t u n n e l i n g i n N S N t r i l a y e r s : c o l l e c t i v e c h a n n e l p r o b e d b y a p h a s e g r a d i e n t
B ) S u b g a p t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n c h a r g e d e n s i t y w a v e s
B . 1 . W e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g p i c t u r e
B . 2 . C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t , m a i n r e s u l t s o n t h e D e l f t e x p e r i m e n t w i t h s u p e r c o n d u c t o r s
C ) J o s e p h s o n e e c t t h r o u g h a c h a r g e d e n s i t y w a v e
B . 1 . C h a r g e d e n s i t y w a v e
B . 2 . S p i n d e n s i t y w a v e
D ) E n e r g y r e l a x a t i o n i n s p i n d e n s i t y w a v e s
D . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y : t w o l e v e l s y s t e m s v e r s u s S c h o t t k y a n o m a l y
D . 1 . 1 E x p e r i m e n t s ( L a s j a u n i a s , B i l j a k o v i c , M o n c e a u e t a l ) : Cp(T) T2
s p e c i c h e a t a s f o r t w o - l e v e l s y s t e m s
D . 1 . 2 T h e o r y : G e n e r a l i z a t i o n o f t h e L a r k i n - O v c h i n n i k o v l e v e l s p l i t t i n g f o r l o c a l d e f e c t s i n a C D W .
D . 2 . C o u p l i n g t o a m a g n e t i c e l d i n a c o m m e n s u r a t e s p i n d e n s i t y w a v e
D . 2 . 1 R e c e n t e x p e r i m e n t s ( L a s j a u n i a s , S a h l i n g , R e m e n y i ) : e v i d e n c e o f a n e w g r o u n d s t a t e a f t e r t h e a p p l i c a t i o n o f a
m a g n e t i c e l d
D . 2 . 2 T h e o r y : t r a n s i t i o n t o a d e n s i t y w a v e g l a s s w i t h a r a n d o m p h a s e a n d s p i n d e g r e e s o f f r e e d o m o n t h e s o l i t o n s
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O u t l i n e
A ) N I N a n d N S N s t r u c t u r e s b e y o n d l o w e s t o r d e r p e r t u r b a t i o n i n t h e i n t e r f a c e t r a n s p a r e n c i e s
A . 1 . N o r m a l t u n n e l j u n c t i o n s : a l r e a d y a c o l l e c t i v e c h a n n e l
A . 2 . W e a k l o c a l i z a t i o n - l i k e t u n n e l i n g i n N S N t r i l a y e r s : c o l l e c t i v e c h a n n e l p r o b e d b y a p h a s e g r a d i e n t
B ) S u b g a p t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n c h a r g e d e n s i t y w a v e s
B . 1 . W e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g p i c t u r e
B . 2 . C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t , m a i n r e s u l t s o n t h e D e l f t e x p e r i m e n t w i t h s u p e r c o n d u c t o r s
C ) J o s e p h s o n e e c t t h r o u g h a c h a r g e d e n s i t y w a v e
B . 1 . C h a r g e d e n s i t y w a v e
B . 2 . S p i n d e n s i t y w a v e
D ) E n e r g y r e l a x a t i o n i n s p i n d e n s i t y w a v e s
D . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y : t w o l e v e l s y s t e m s v e r s u s S c h o t t k y a n o m a l y
D . 1 . 1 E x p e r i m e n t s ( L a s j a u n i a s , B i l j a k o v i c , M o n c e a u e t a l ) : Cp(T) T
2s p e c i c h e a t a s f o r t w o - l e v e l s y s t e m s
D . 1 . 2 T h e o r y : G e n e r a l i z a t i o n o f t h e L a r k i n - O v c h i n n i k o v l e v e l s p l i t t i n g f o r l o c a l d e f e c t s i n a C D W .
D . 2 . C o u p l i n g t o a m a g n e t i c e l d i n a c o m m e n s u r a t e s p i n d e n s i t y w a v e
D . 2 . 1 R e c e n t e x p e r i m e n t s ( L a s j a u n i a s , S a h l i n g , R e m e n y i ) : e v i d e n c e o f a n e w g r o u n d s t a t e a f t e r t h e a p p l i c a t i o n o f a
m a g n e t i c e l d
D . 2 . 2 T h e o r y : t r a n s i t i o n t o a d e n s i t y w a v e g l a s s w i t h a r a n d o m p h a s e a n d s p i n d e g r e e s o f f r e e d o m o n t h e s o l i t o n s
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A . 1 . ) N o r m a l t u n n e l j u n c t i o n s
H y p o t h e s i s a b o u t t h e i n s u l a t o r : B C S - l i k e d i s p e r s i o n r e l a t i o n p o p u l a t e d b y g e n u i n e
e l e c t r o n s a n d h o l e s
kk FF
Ene
rgy
Wavevector
Filled states
Empty states
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L e t ' c o m e b a c k t o t h e C a r o l i e t a l . t r a n s p o r t f o r m u l a : a n e l e c t r o n c a n b e
t r a n s m i t t e d f r o m l e f t t o r i g h t a c r o s s t h e i n s u l a t o r , a n d a t t h e s a m e t i m e a h o l e i s
t r a n s m i t t e d f r o m r i g h t t o l e f t .
AG,
GR,a,a b,b
e e
hh
a b NIN
time t1
time t2
T h e e l e c t r o n a n d h o l e c a n b o u n c e a t t h e i n t e r f a c e s
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=
+
+
N NI N N
N
N
NN
N
N
I
I
I
I
+ + ...
Local
one interface
bouncing at
Boucing
involving
both
interfaces
e e
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A ) P r o c e s s e s n o t c o u p l i n g t o a m a g n e t i c u x
Direct propagation, no bouncing
IN N
Local bouncing at one interfacee
h
h
e
Magnetic flux
B ) W e a k l o c a l i z a t i o n - l i k e p r o c e s s e s w i t h h/2e - p e r i o d i c m a g n e t o c o n d u c t a n c e
e
h
h
h
The hole bounces between the two interfaces
N I N
W e a k l o c a l i z a t i o n - l i k e l o o p s a c r o s s t h e e n t i r e s t r u c t u r e . A d v a n c e d - A d v a n c e d a n d
R e t a r d e d - R e t a r d e d t r a n s m i s s i o n m o d e s . h/2e m o d u l a t i o n s o f t h e c o n d u c t a n c e .
T y p e s e t b y F o i l T
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O u t l i n e
A ) N I N a n d N S N s t r u c t u r e s b e y o n d l o w e s t o r d e r p e r t u r b a t i o n i n t h e i n t e r f a c e t r a n s p a r e n c i e s
A . 1 . N o r m a l t u n n e l j u n c t i o n s : a l r e a d y a c o l l e c t i v e c h a n n e l
A . 2 . W e a k l o c a l i z a t i o n - l i k e t u n n e l i n g i n N S N t r i l a y e r s : c o l l e c t i v e c h a n n e l p r o b e d b y a p h a s e g r a d i e n t
B ) S u b g a p t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n c h a r g e d e n s i t y w a v e s
B . 1 . W e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g p i c t u r e
B . 2 . C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t , m a i n r e s u l t s o n t h e D e l f t e x p e r i m e n t w i t h s u p e r c o n d u c t o r s
C ) J o s e p h s o n e e c t t h r o u g h a c h a r g e d e n s i t y w a v e
B . 1 . C h a r g e d e n s i t y w a v e
B . 2 . S p i n d e n s i t y w a v e
D ) E n e r g y r e l a x a t i o n i n s p i n d e n s i t y w a v e s
D . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y : t w o l e v e l s y s t e m s v e r s u s S c h o t t k y a n o m a l y
D . 1 . 1 E x p e r i m e n t s ( L a s j a u n i a s , B i l j a k o v i c , M o n c e a u e t a l ) : Cp(T) T
2s p e c i c h e a t a s f o r t w o - l e v e l s y s t e m s
D . 1 . 2 T h e o r y : G e n e r a l i z a t i o n o f t h e L a r k i n - O v c h i n n i k o v l e v e l s p l i t t i n g f o r l o c a l d e f e c t s i n a C D W .
D . 2 . C o u p l i n g t o a m a g n e t i c e l d i n a c o m m e n s u r a t e s p i n d e n s i t y w a v e
D . 2 . 1 R e c e n t e x p e r i m e n t s ( L a s j a u n i a s , S a h l i n g , R e m e n y i ) : e v i d e n c e o f a n e w g r o u n d s t a t e a f t e r t h e a p p l i c a t i o n o f a
m a g n e t i c e l d
D . 2 . 2 T h e o r y : t r a n s i t i o n t o a d e n s i t y w a v e g l a s s w i t h a r a n d o m p h a s e a n d s p i n d e g r e e s o f f r e e d o m o n t h e s o l i t o n s
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B . 1 . ) T u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n C D W s
Bcurrent flow
0
xy
z
x
y
0
chain (3)
chain (1)
chain (2)
(b)(a)
nanohole
S l i d i n g m o t i o n f a r a w a y f r o m t h e n a n o h o l e c o n v e r t e d i n e l e c t r o n t u n n e l i n g a r o u n d
t h e n a n o h o l e C h a r g e a c c u m u l a t i o n i n t h e i n t e r r u p t e d c h a i n s
I =e
h
0
T()d() w i t h > s u b g a p t u n n e l i n g f o r < .
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S u b g a p t u n n e l i n g t r a n s m i s s i o n c o e c i e n t
0 1
x
x
0 1chain (3)
chain (2)
y x x y
A
A
A
R
A
A
R
R
(2) (2) (2) (2)
chain (1)
h/2ep e r i o d i c . W h a t a b o u t s m a l l i n t e r c h a i n c o u p l i n g s ?
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N o r m a l r e g i o n a r o u n d a n a n o h o l e
A s p o i n t e d o u t b y V i s s c h e r e t a l . i n t h e i r ' 0 0 R a n d o m M a t r i x T h e o r y p a p e r , t h e d a m a g e d n o r m a l
r e g i o n a r o u n d t h e n a n o h o l e i s n o r m a l .
Nanohole
A A
around the nanoholeNormal region
A Advancedretardedtransmission mode
A
A
R
R
R
R
R
R
A
A
Advancedadvanced
transmission mode
T h e l e v e l s p a c i n g
p l a y s t h e r o l e o f a g a p a n d t h e p r e v i o u s m o d e l s t i l l a p p l i e s .
f o r a n o r m a l r e g i o n o f s i z e
.M o r e o v e r e v e n w i t h d i s o d e r , H i k a m i b o x e s c o n t a i n a d v a n c e d - a d v a n c e d a n d r e t a r d e d - r e t a r d e d d i u s i o n m o d e s
s t a n d a r d w e a k l o c a l i z a t i o n d o e s n o t a p p l y .
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B . 2 . ) C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t
1 . A b s e n c e o f m a g n e t o r e s i s t a n c e o s c i l l a t i o n s w i t h o u t n a n o h o l e s
2 . A b s e n c e o f m a g n e t o r e s i s t a n c e o s c i l l a t i o n s w i t h n a n o h o l e s b u t w i t h o u t s l i d i n g
m o t i o n
3 . h/2e m a g n e t o r e s i s t a n c e o s c i l l a t i o n s w i t h n a n o h o l e s a n d w i t h s l i d i n g m o t i o n
4 . P o s i t i v e m a g n e t o r e s i s t a n c e a t l o w e l d w i t h n a n o h o l e s
5 . M a g n e t o r e s i s t a n c e o s c i l l a t i o n s a t h i g h t e m p e r a t u r e ( 52 K ) b e c a u s e t h e e n - e r g y / t e m p e r a t u r e s c a l e i s
o r
.
C o n c l u s i o n : T h e m o d e l o f 1 D i n s u l a t o r s a n d t h e m o d e l o f n o r m a l r e g i o n
s u g g e s t t h a t t h e C D W c o n d e n s a t e i s n o t i n v o l v e d .
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T o c o n c l u d e t h i s p a r t o f t h e s e m i n a r :
I t l o o k s l i k e w e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g i s t h e c l u e t o t h e L a t y s h e v
e x p e r i m e n t .
T h e m e c h a n i s m r e l i e s o n t h e s l i d i n g m o t i o n ( e m i s s i o n o f q u a s i p a r t i c l e s ) a n d
o n t h e q u a s i - o n e d i m e n s i o n a l i t y ( c h a r g e a c c u m u l a t i o n ) .
B u t t h e t u n n e l i n g e v e n t i n i t s e l f d o e s n o t c o u p l e t o c o l l e c t i v e m o t i o n ( t u n n e l i n g
t h r o u g h t h e d a m a g e d r e g i o n o f s i z e ) .
S o , t h e L a t y s h e v e x p e r i m e n t d o e s n o t p r o b e t h e q u a n t u m m e -
c h a n i c a l C D W g r o u n d s t a t e . A n y p o s s i b i l i t y o f p r o b i n g p h a s e
c o h e r e n c e o f a C D W : J o s e p h s o n e e c t t h r o u g h a C D W ( o r a
S D W ) ?
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O u t l i n e
A ) N I N a n d N S N s t r u c t u r e s b e y o n d l o w e s t o r d e r p e r t u r b a t i o n i n t h e i n t e r f a c e t r a n s p a r e n c i e s
A . 1 . N o r m a l t u n n e l j u n c t i o n s : a l r e a d y a c o l l e c t i v e c h a n n e l
A . 2 . W e a k l o c a l i z a t i o n - l i k e t u n n e l i n g i n N S N t r i l a y e r s : c o l l e c t i v e c h a n n e l p r o b e d b y a p h a s e g r a d i e n t
B ) S u b g a p t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n c h a r g e d e n s i t y w a v e s
B . 1 . W e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g p i c t u r e
B . 2 . C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t , m a i n r e s u l t s o n t h e D e l f t e x p e r i m e n t w i t h s u p e r c o n d u c t o r s
C ) J o s e p h s o n e e c t t h r o u g h a c h a r g e d e n s i t y w a v e
B . 1 . C h a r g e d e n s i t y w a v e
B . 2 . S p i n d e n s i t y w a v e
D ) E n e r g y r e l a x a t i o n i n s p i n d e n s i t y w a v e s
D . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y : t w o l e v e l s y s t e m s v e r s u s S c h o t t k y a n o m a l y
D . 1 . 1 E x p e r i m e n t s ( L a s j a u n i a s , B i l j a k o v i c , M o n c e a u e t a l ) : Cp(T) T
2s p e c i c h e a t a s f o r t w o - l e v e l s y s t e m s
D . 1 . 2 T h e o r y : G e n e r a l i z a t i o n o f t h e L a r k i n - O v c h i n n i k o v l e v e l s p l i t t i n g f o r l o c a l d e f e c t s i n a C D W .
D . 2 . C o u p l i n g t o a m a g n e t i c e l d i n a c o m m e n s u r a t e s p i n d e n s i t y w a v e
D . 2 . 1 R e c e n t e x p e r i m e n t s ( L a s j a u n i a s , S a h l i n g , R e m e n y i ) : e v i d e n c e o f a n e w g r o u n d s t a t e a f t e r t h e a p p l i c a t i o n o f a
m a g n e t i c e l d
D . 2 . 2 T h e o r y : t r a n s i t i o n t o a d e n s i t y w a v e g l a s s w i t h a r a n d o m p h a s e a n d s p i n d e g r e e s o f f r e e d o m o n t h e s o l i t o n s
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A b s e n c e o f J o s e p h s o n c u r r e n t t h r o u g h a c h a r g e d e n s i t y w a v e
SS
CDW chains
What is the distance between the
superconductors for establishinga Josephson effect ?
CDW or SDW
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A n d r e e v r e e c t i o n a t a N S i n t e r f a c e
*
*
*
*
**
***
*
eh
e
e
h
h
SuperconductorN
ormalmetal
E n e r g y o f a n e l e c t r o n - h o l e p a i r a r r i v i n g o n a n i m p u r i t y a t z e r o b i a s : Vimp(e,
h,) = 0 e l e c t r o n - h o l e p a i r s d o n o t d e p h a s e a t z e r o b i a s
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S - C D W - S j u n c t i o n
A m a x i m u m i n t h e e l e c t r o n d e n s i t y c o r r e s p o n d s t o a m i n i m u m i n t h e h o l e d e n s i t y :
e, = 0 + 1 cos(Qx + ) a n d h, = 0 1 cos(Qx + )
W e d e d u c e Vimp(e, h,) = 0 d e p h a s i n g o f e l e c t r o n - h o l e p a i r b y a s i n g l e i m p u r i t y . C o n r m e d b y m i c r o s c o p i c c a l c u l a t i o n s o f t h e d i u s i o n m o d e s .
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h
e e
h
*
b,b
a,a
a b
time t1time t
2,A
R
,
g
g=0
S CDW S
SI
SPINDOWN HOLE
SPINUP ELECTRON
W h a t a b o u t s p i n d e n s i t y w a v e s ?
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S p i n d e n s i t y w a v e s
e,(x) = 0 + 1 cos(Qx + ) e,(x) = 0 1 cos(Qx + )
( )x
x
spindown
spinup
T h e r e f o r e e,(x) = h,(x)
A n d r e e v p a i r s d o n o t d e p h a s e .
T h e t w o s u p e r c o n d u c t i n g e l e c t r o d e s c a n b e s e p a r a t e d b y SDW.
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C o m p a r i s o n w i t h e x p e r i m e n t s ( S y n c h e n k o , M o n c e a u , J P C M ' 0 3 )
M a x i m u m o f r e s i s t a n c e f o r a S - C D W j u n c t i o n w i t h o u t i n s u l a t i n g b a r r i e r s ( c u r v e s
c , d , e ) n o p e n e t r a t i o n o f A n d r e e v p a i r s i n a C D W .
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C o n c l u s i o n o f t h i s p a r t o f t h e s e m i n a r :
. . . . T h e J o s e p h s o n e e c t p r o v i d e s n o e v i d e n c e o f p h a s e c o h e r e n c e o f a C D W .
W h a t a b o u t g o i n g t o v e r y l o w t e m p e r a t u r e s ?
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O u t l i n e
A ) N I N a n d N S N s t r u c t u r e s b e y o n d l o w e s t o r d e r p e r t u r b a t i o n i n t h e i n t e r f a c e t r a n s p a r e n c i e s
A . 1 . N o r m a l t u n n e l j u n c t i o n s : a l r e a d y a c o l l e c t i v e c h a n n e l
A . 2 . W e a k l o c a l i z a t i o n - l i k e t u n n e l i n g i n N S N t r i l a y e r s : c o l l e c t i v e c h a n n e l p r o b e d b y a p h a s e g r a d i e n t
B ) S u b g a p t u n n e l i n g v i a q u a n t u m i n t e r f e r e n c e e e c t i n c h a r g e d e n s i t y w a v e s
B . 1 . W e a k l o c a l i z a t i o n - l i k e s u b g a p t u n n e l i n g p i c t u r e
B . 2 . C o m p a r i s o n w i t h t h e L a t y s h e v e x p e r i m e n t , m a i n r e s u l t s o n t h e D e l f t e x p e r i m e n t w i t h s u p e r c o n d u c t o r s
C ) J o s e p h s o n e e c t t h r o u g h a c h a r g e d e n s i t y w a v e
B . 1 . C h a r g e d e n s i t y w a v e
B . 2 . S p i n d e n s i t y w a v e
D ) E n e r g y r e l a x a t i o n i n s p i n d e n s i t y w a v e s
D . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y : t w o l e v e l s y s t e m s v e r s u s S c h o t t k y a n o m a l y
D . 1 . 1 E x p e r i m e n t s ( L a s j a u n i a s , B i l j a k o v i c , M o n c e a u e t a l ) : Cp(T) T
2s p e c i c h e a t a s f o r t w o - l e v e l s y s t e m s
D . 1 . 2 T h e o r y : G e n e r a l i z a t i o n o f t h e L a r k i n - O v c h i n n i k o v l e v e l s p l i t t i n g f o r l o c a l d e f e c t s i n a C D W .
D . 2 . C o u p l i n g t o a m a g n e t i c e l d i n a c o m m e n s u r a t e s p i n d e n s i t y w a v e
D . 2 . 1 R e c e n t e x p e r i m e n t s ( L a s j a u n i a s , S a h l i n g , R e m e n y i ) : e v i d e n c e o f a n e w g r o u n d s t a t e a f t e r t h e a p p l i c a t i o n o f a
m a g n e t i c e l d
D . 2 . 2 T h e o r y : t r a n s i t i o n t o a d e n s i t y w a v e g l a s s w i t h a r a n d o m p h a s e a n d s p i n d e g r e e s o f f r e e d o m o n t h e s o l i t o n s
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D . 1 . 1 . A s i n g l e s t r o n g p i n n i n g i m p u r i t y .
D . 1 . 1 T h e e x p e r i m e n t s : T h e s a m p l e i s c o n n e c t e d t o a t h e r m a l r e s e r v o i r b y a w e a k l i n k
u s e d t o w a r m t h e s y s t e m . T h e t e m p e r a t u r e o f t h e s a m p l e m e a s u r e d a s a f u n c t i o n o f t i m e f o r
d i e r e n t v a l u e s o f a t h e h e a t p u l s e
time00 tw
Q(t)
T(t)
T0
0 tw t +w
time
Experimental signalSample
Thermome
ter
weak link
Thermal
Reservoir
Q(t)
T h e s y s t e m i s e q u i l i b r a t e d a t T0 ! ( i n t e r r u p t e d a g e i n g ) . T h e w a i t i n g t i m e tw c a n b e l o n g e r t h a n
t h e l o n g e s t r e l a x a t i o n t i m e ( e q u i l i b r i u m r e l a x a t i o n ) .
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P i n n i n g o f a C D W ( o r S D W )
A t l o w t e m p e r a t u r e t h e p h a s e o f t h e C D W i s f r o z e n e x c e p t f o r l o c a l i z e d p h a s e d e f e c t s . T h e
e n e r g y i s t h e r e s u l t o f
1 . T h e e l a s t i c e n e r g y t h a t p e n a l i z e s l a r g e p h a s e g r a d i e n t s .
2 . T h e c o m m e n s u r a t i o n e n e r g y t h a t t e n d s t o x t h e p h a s e t o t h e d i s c r e t e v a l u e s
..., 0, 2, 4, ...
W i t h 1 . a n d 2 . w e h a v e a a t p h a s e i n t h e g r o u n d s t a t e : (x) = 2n w i t h n a n i n t e g e r . T h e e x c i t a t i o n s a r e p a i r s o f s o l i t o n s / a n t i s o l i t o n s
2 (n+1)
2 n
( )x
x
Soliton Antisoliton
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3 . H o w e v e r t h e i m p u r i t i e s t e n d t o x l o c a l l y t h e v a l u e o f t h e p h a s e . T h i s c a n
r e s u l t i n a d i p o l e ( o r b i s o l i t o n ) = b o u n d s t a t e o f a s o l i t o n a n d a n a n t i s o l i t o n . T h e
s y m m e t r y (xi) (xi) i s b r o k e n b y t h e i m p u r i t y p i n n i n g t e r m
Dipole
Antidipole
( )x
2(n1)
2 n
2(n+1)
unphysical
x
Impurity
( )xi
E[ ]( )i
x
E0
E + E0
Dipole
Antidipole
T h i s d e n e s a n e e c t i v e t w o - l e v e l s y s t e m w i t h a s p l i t t i n g E 4ES, w i t h ESt h e e n e r g y o f a 2 s o l i t o n . E i s i n d e p e n d e n t o n t h e p i n n i n g e n e r g y . T h e b a r r i e r i s r o u g h l y t h e p i n n i n g e n e r g y .
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D . 2 . E e c t o f a m a g n e t i c e l d i n a c o m m e n s u r a t e S D W
D . 2 . 1 E x p e r i m e n t a l s t u d y ( b y J . C . L a s j a u n i a s , G . R e m e n y i , S . S a h l i n g ) o f t h e e q u i l i b r i u m
h e a t r e l a x a t i o n o f ( T M T T F ) 2 B r i n a m a g n e t i c e l d ( p o s s i b l e b e c a u s e o f t h e n a r r o w r e l a x a t i o n
t i m e s p e c t r u m ) . E v i d e n c e o f a v e r y s t a b l e n e w b r a n c h i n t h e s p e c i c h e a t
( T = 92 m K ) :
1
10
102
103
104
10-2
10-1
1 10hc
Specificheat(mJ/mo
lK)
Magnetic field (T)
Branch 1
Branch 2
Bisolitons (spin-up)
Bisolitons (total)
R . M l i n , J . C . L a s j a u n i a s , S . S a h l i n g , G . R e m e n y i a n d K . B i l j a k o v i c P R L 9 7 , 2 2 7 2 0 3 ( ' 0 6 ) . A n y
e x p l a n a t i o n ?
T y p e s e t b y F o i l T
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D . 2 . 2 A s i n g l e 2 s o l i t o n i n a Z e e m a n e l d
S o l i t o n s a n d a n t i s o l i t o n s c a r r y a s p i n !
( )x
x0
2
h
spin soliton
spin soliton
no soliton
hc
0
spin or spin0
ES
Energy
T h e S D W g r o u n d s t a t e i s u n s t a b l e f o r h > hc.
T y p e s e t b y F o i l T
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N u c l e a t i o n o f d e c o n n e d p a i r s o f s o l i t o n a n d a n t i s o l i t o n a t a s t r o n g p i n n i n g i m p u r i t y
-0.75
-0.5
-0.25
0
0.25
-2 -1 0 1 2
Potentialenergy(K)
i / 2
h = 0 T
(a)
-0.75
-0.5
-0.25
0
0.25
-2 -1 0 1 2
i / 2
h = 7.3 T
(b)
(2)
(3)
(1)
( 1 ) ( 2 ) : t r a n s i t i o n b e t w e e n a n a n t i b i s o l i t o n a n d a b i s o l i t o n .
( 2 ) ( 3 ) : n u c l e a t i o n o f a n a d d i t i o n a l s o l i t o n - a n t i s o l i t o n p a i r ( g a i n i n Z e e m a n e n e r g y ) .
x x x
( ) ( )( )x x x
(1) (2)
(3)2
Antibisoliton BisolitonAntibisoliton+
soliton/antisoliton pair
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S p i n e n t r o p y o f a S D W g l a s s
( )
( )
( )
x
x
x
x
x
x
h>h c
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G e n e r a l c o n c l u s i o n s
1 . T u n n e l i n g v i a w e a k l o c a l i z a t i o n - l i k e q u a n t u m i n t e r f e r e n c e e e c t t h r o u g h a n y
g a p p e d s y s t e m .
2 . P r o v i d e s a n e x p l a n a t i o n t o t h e L a t y s h e v e x p e r i m e n t o n C D W s ( a n d t o t h e D e l f t e x p e r i m e n t
o n c r o s s e d A n d r e e v r e e c t i o n ) .
3 . C h a r g e a c c u m u l a t i o n c o u p l e s s u b g a p t r a n s p o r t t o t h e C D W s l i d i n g m o t i o n . Q u a n t u m
i n t e r f e r e n c e e e c t v i a t h e d a m a g e d r e g i o n a r o u n d a n a n o h o l e s u g g e s t s t h a t t h e C D W
c o n d e n s a t e i s n o t i n v o l v e d i n t h e e x p e r i m e n t .
4 . P h a s e c o h e r e n c e o f a c h a r g e d e n s i t y w a v e c a n n o t b e p r o b e d b y t h e J o s e p h s o n e e c t .
5 . D e s c r i p t i o n o f e n e r g y r e l a x a t i o n i n C D W s a n d S D W s o n t h e b a s i s o f t h e L a r k i n - O v c h i n n i k o v
l e v e l s p l i t t i n g m e c h a n i s m . T r a n s i t i o n t o a d e n s i t y w a v e g l a s s u p o n a p p l y i n g a m a g n e t i c e l d
( t h ) . V e r y p e r s i s t a n t m e t a s t a b l e b r a n c h i n t h e s p e c i c h e a t ( e x p ) .
S o , n o e v i d e n c e o f t h e q u a n t u m m e c h a n i c a l f e a t u r e s o f t h e
C D W g r o u n d s t a t e i n t h e d i s c u s s e d s i t u a t i o n s . F i n a l t r a n s p a r e n c y
n o t t o b e f o r g o t t e n . . . . . . . . . .
T y p e s e t b y F o i l T
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R e f e r e n c e s
o n t h e L a t y s h e v e x p e r i m e n t : S . D u h o t , R . M l i n , P h y s . R e v . B 7 6 , 1 8 4 5 0 3
( 2 0 0 7 )
o n S - C D W j u n c t i o n s : S . D u h o t , R . M l i n , E P J B 5 5 ( 2 0 0 7 )
o n s o l i t o n d i p o l e s : R . M l i n , J . C . L a s j a u n i a s , S . S a h l i n g , G . R e m e n y i , K . B i l j a k o v i c ,
P R L 9 7 , 2 2 7 2 0 3 ( 2 0 0 6 ) .
A c k n o w l e d g m e n t s
T h e M o n c e a u t e a m + S . B r a z o v s k i i + J . P . B r i s o n , P . R o d i r e ( o n - g o i n g p r o j e c t ) .
T h e G r e n o b l e t h e o r e t i c i a n s : R . W h i t n e y + m a n y d i s c u s s i o n s w i t h B . D o u o t , D .
F e i n b e r g , S . F l o r e n s , M . H o u z e t , F . P i s t o l e s i , J . R a n n i n g e r o n t h e s u p e r c o n d u c t i n g
s i d e o f t h e p r o b l e m
T y p e s e t b y F o i l T
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