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HAL Id: tel-00684262

https://tel.archives-ouvertes.fr/tel-00684262

Submitted on 31 Mar 2012

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Spectroscopies locales sur des nanostructures hybrides hors équilibre

Thomas Quaglio

To cite this version:

Thomas Quaglio. Spectroscopies locales sur des nanostructures hybrides hors équilibre. Autre [cond-

mat.other]. Université de Grenoble, 2012. Français. �NNT : 2012GRENY006�. �tel-00684262�

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THÈSE

Pour obtenir le grade de

DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE

Spécialité : Physique/Nanophysique

Arrêté ministériel : 7 août 2006

Présentée par

Thomas Quaglio

Thèse dirigée par Hervé Courtois

préparée au sein de l’Institut Néel et de l’École doctorale de Physique

Spectroscopies locales sur des nanostructures supraconductrices hybrides hors équilibre

Thèse soutenue publiquement le 19 janvier 2012, devant le jury composé de :

Klaus Hasselbach

CNRS, Institut Néel, Président

Philippe Lafarge

CNRS/Université Parid Diderot, MPQ, Rapporteur

Tristan Cren

CNRS, INSP, Rapporteur

Anne Anthore

CNRS/Université Parid Diderot, LPN, Examinateur

Clemens Winkelmann

INPG/CNRS Institut, Néel, Examinateur

Hervé Courtois

UJF/CNRS, Institut Néel, Directeur de thèse

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Ψ U l

− ~

2

2m

∂z

2

Ψ(z) + U (z)Ψ(z) = EΨ(z) 0 < z < l

Ψ(z) = Ψ(0)exp −

p 2m(U − E)

~ z

!

p = |

Ψ(0)Ψ(l)

|

2

(15)

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(16)

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(E)n

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(E)

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+∞

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(E)dE

n

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∂V (V ) ∝ − ˆ

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f (E) = 1 exp

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kBT

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∂I

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e

(E

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(17)

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(18)

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(19)

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(21)

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(22)

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&# '&%( )"&2/="&# #&+-/!,# #&"!,- +!,#*+"3&# P %,& '&#+"/)-/!, B3,3"*1&

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%, #%)"*+!,'%+-&%"8 >,A, ,!%# *0!"'&"!,# 1& +!2)!"-&2&,- &, -"*,#)!"- '&#

6!,+-/!,# 6!#&)7#!, GHG &, )*"-/+%1/&"4 1&%"# +*"*+-3"/#-/$%&# +!%"*,-:-&,#/!,4 1& +!%"*,- +"/-/$%&4 1& +!%"*,- '& "&)/3B&*B& &- 1& )73,!2=,& '@7Q#-3"3#/#8

!" #$%& '()%*+)(,

R*,# 1&# #%)"*+!,'%+-&%"#4 1&# 31&+-"!,# )"!+7&# '& 1@3,&"B/& '& S&"2/ #& +!,'&,#&,-

&, )*/"&# '& 9!!)&" JTN $%/ )&%E&,- *1!"# <-"& '3+"/-&# )*" %,& %,/$%& .!,+-/!, '@!,'& Ψ = | Ψ | e

!"##" $%&'#(%& )*%&)" )"+ ,-(."+ )" !%%,". - /#/ )*-0%.) (&#.%)1(#" "& 2345 ,-. 6(&701.8 "# 9-&)-1 :;5< -="' )"+ '%&+()/.-#(%&+ /&".>

8/#(?1"+ @AA" +*/#"&) )-&+ #%1# A" +1,.-'%&)1'#"1.B '" ?1( A1( '%&$C." 1& '%D>

,%.#"D"&# ?1-&#(?1" D-'.%+'%,(?1" 9*"E"# F%+",G+%& ,".D"# )" +*"& $-(." 1&"

()/" #.C+ ,-A,-0A" HA - /#/ ,./)(# ,-. F%+",G+%& "& 23IJ :22B 2J< "# $1# D"+1./

J4

(27)

Φ I

s

I

S

= I

c

sinΦ I

c

I = I

S

+ I

N

I

N

∂Φ

∂t = 2e

~ V

e ~ V = 2∆

∆ ≈

(28)

!"! #$$#% &'(#)*('+ !

"# $%&' '&(() I $) *&+,-'. .,-/),0-'. $- 1&'*.#&' ). V $- .)'0#&' 2 0)0 3&,')04

$)0 $&#0 5) 6#,*77&8 '&+0 5&'')'.

I = I

c

sinΦ + V

R + C ∂V

∂t 9 :;<

=' +.#$#0-'. $- 0)*&'5) >?+-.#&' @&0)A70&' 9>?+-.#&' : <4 &' &3.#)'. B-*#$)()'. C C

~ 2e

2

2

Φ

∂t

2

+ 1 R

~ 2e

2

∂Φ

∂t + E

J

sinΦ = E

J

I

I

C

9 :D<

&E E

J

=

~2eIC

)0. $%>'),F#) @&0)A70&': G$ )0. A,-.#?+) 5) 5>H'#, $%>'),F#) 5) *7-,F) 5) $- 1&'*.#&' E

C

=

2Ce2

: I' ,)*&''-J. 5-'0 $%>?+-.#&' :D $%>?+-.#&' 5%>/&$+.#&' .)(A&,)$$) 5%+' &0*#$$-.)+, '&' $#'>-#,): K) 0L0.M() A)+. -+00# N.,) /+ *&(() +') A-,.#*+$) 5) (-00) m = C "

~

2e

2

). 5) A&0#.#&' Φ >/&$+-'. 5-'0 +' A&.)'.#)$

)' .O$) &'5+$>) U (Φ) = − E

J

cosΦ +

II

C

Φ

: K%)0. +' A&.)'.#)$ 0#'+0&P5-$ 5&'.

$- A)'.) (&L)'') )0. 5>.),(#'>) A-, $) *&+,-'. 5%#'1)*.#&' I 9HF+,) :Q<: "# $) 0L0.M() >.-#. *$-00#?+)4 $- A-,.#*+$) 0%>*7-AA),-#. $&,0?+) I = I

C

4 *%)0. 2 5#,)

$&,0?+) $- 7-+.)+, 5) $- 3-,,#M,) 0%-''+$): =' ,>-$#.>4 $- A-,.#*+$) A)+. 0%>*7-AA), +' A)+ -/-'.4 0&#. F,R*) -+S T+*.+-.#&'0 .7),(#?+)04 0&#. A-, )8). .+'')$: U)

*&+,-'. (-S#(+( ()0+,> ?+) $%&' -AA)$$) *&+,-'. 5%>*7-AA)()'. )0. 5&'*

A$+0 B-#3$): I' A)+. ,).,&+/), $) *&+,-'. *,#.#?+) 5%+') 1&'*.#&' @&0)A70&' )'

>.+5#-'. $- 0.-.#0.#?+) 5+ *&+,-'. 5%>*7-AA)()'.: V A-,.#, 5+ (&()'. &E $- A-,.#*+$) 0) 5>A$-*)4 $- A7-0) /-,#) ). +') .)'0#&' -AA-,-J.: U- 1&'*.#&' )0. -$&,0 5-'0 $%>.-. ,>0#0.#B W $- .)'0#&' ). $) *&+,-'. &0*#$$)'. 2 $- A+$0-.#&'

2e~

V :

I' A)+. 5>H'#, *&(() A&+, $)0 &0*#$$-.)+,0 $#'>-#,)0 +' B-*.)+, 5) ?+-$#.>

Q = ω

p

RC -/)* ω

p

=

~1

√ 8E

J

E

C

). 5#8>,)'*#), 5)+S .LA)0 5) 1&'*.#&'0: U)0 1&'*.#&'0 0+,X-(&,.#)0 A&+, $)0?+)$$)0 Q ≪ 1 ). $)0 1&'*.#&'0 0&+0X-(&,.#)0

$&,0?+) Q ≫ 1 C

!"#$%!"& &!'&()*!+$%,&

Y&+, Q ≫ 14 +') B&#0 ?+) $) *&+,-'. *,#.#?+) - >.> B,-'*7#4 $- A-,.#*+$) /#,.+)$$) 5>/-$) $- A)'.) 2 +') /#.)00) ,)$-.#/)()'. #(A&,.-'.): U- .)'0#&' (&L)'')4

?+# )0. $- F,-'5)+, ?+) '&+0 ()0+,&'0 )8)*.#/)()'.4 )0. -$&,0 >F-$) -+ F-A

< V >= ∆/e: "# )'0+#.) &' 5#(#'+) $) *&+,-'. 1+0.) )' 5)00&+0 5+ *&+,-'.

*,#.#?+)4 $- 5#00#A-.#&' '%)0. A-0 0+Z0-'.) A&+, ,)A#>F), $- A-,.#*+$): U- 1&'*.#&'

@&0)A70&' A)+. N.,) /+) *&(() +') #'5+*.-'*) B&,.)()'. '&' $#'>-#,)4 ). *) A7>'&(M') 0) .,-5+#. A-, 5)0 &0*#$$-.#&'0 5) $- ,>A-,.#.#&' 5+ *&+,-'. )'.,) $- 1&'*.#&' @&0)A70&' ). $- *-A-*#.>: U- 1&'*.#&' )0. -$&,0 7L0.>,>.#?+): =$$) ,)/#)'.

5-'0 $%>.-. '&' 5#00#A-.#B A&+, +' *&+,-'. 5) ,)A#>F)-F) I

r

≈ 4I

c

/πQ 3)-+*&+A A$+0 B-#3$) ?+) $) *&+,-'. *,#.#?+):

!"#$%!"& &'+()*!+$%,&

U&,0?+) Q ≪ 14 $%)SA,)00#&' :D 0) 0#(A$#H) )'

(29)

∂Φ

∂t = 2eI

C

R

~ I

I

C

− sinΦ

Φ(t)

< V >= R

N

p I

2

− I

c2

V ≪ ∆

C ∼ 10

19

F R = 3 Ω I

c

= 10

ω

p

≈ 2.10

14

Q ≈ 10

4

(30)

! ! "#$%&'()$"&# * +,-..-$ '- /%&0"1"$2 !

! "#$%&'()$*&# + ,-./.$ '. 0%&1*2*$3

! !" #$%&'()*+ ,-.*,/&&0

"# $%&'())( *( +# ,'-)%./( *() 012&3%12) 41)(,')12 '-5$%*() 6%(23 */ &1/,+#7(

(23$( +() )/,$#&12*/&3(/$)8 ./% )( 9#%3 ,#$ +:%23($;<*%#%$( *( $<=(>%12) *:?2@

*$((68 #/> %23($9#&() #6(& +( ;<3#+ 21$;#+A B( ,'<21;C2(8 *<;123$< (2 D!EF ,#$ ?2*$((6 GFEH (3 I#%23@4#;() GFJH8 *<&$%3 +# $<=(>%12 *:/2 <+(&3$12 K +:%23($@

9#&( (23$( /2 ;<3#+ 21$;#+ L (3 /2 )/,$#&12*/&3(/$ IA

M &#/)( */ 7#, *#2) +( )/,$#&12*/&3(/$8 +() <+(&3$12) */ ;<3#+ 21$;#+

&1;,$%) *#2) &(33( 5#2*( *:<2($7%( 2( ,(/6(23 N3$( 3$#2);%) *( 9#O12 )3#2*#$*A P#$ &123$( %+ ,(/3 - #61%$ /2( 3$#2);%))%12 K *(/> ,#$3%&/+() ./% &$<( /2( ,#%$( *(

B11,($ *#2) +( )/,$#&12*/&3(/$A B:()3 &( ;<&#2%);( ./( +:12 21;;( $<=(>%12

*:?2*$((6A "# *()&$%,3%12 +# ,+/) &1/$#23( ()3 *( &12)%*<$($ /2 <+(&3$12 *#2) L

*:<2($7%( E

F

+ǫ #6(& ǫ < ∆ Q∆ <3#23 +( 7#, */ )/,$#&12*/&3(/$ (3 E

F

+:<2($7%(

*( R($;%S8 &:()3@K@*%$( *#2) +( 7#, */ )/,$#&12*/&3(/$8 *( ),%2 s (3 *( 6(&3(/$

*:12*( k

F

+

~vǫF

#6(& v

F

+# 6%3())( *( R($;%A "1$)./:%+ $(2&123$( +:%23($9#&( LI8 %+

()3 $<=<&'% (2 3$1/ *:<2($7%( E

F

− ǫ8 *( 6(&3(/$ *:12*( − k

F

+

~vǫF

(3 *( ),%2 − s (2 3$#2);(33#23 /2( ,#%$( *( B11,($ K +:<2($7%( *( R($;% *#2) +( )/,$#&12*/&3(/$A B(33( $<=(>%12 ()3 &1'<$(23( (3 +1$) *( +# $<=(>%128 +# ,'#)( */ 3$1/ ()3 <7#+( K

&(++( *( +:<+(&3$12 %2&%*(23 ,+/) +( *<,'#)#7( δφ = Φ + arccos(ǫ/∆) 1T Φ ()3 +#

,'#)( ;#&$1)&1,%./( */ )/,$#&12*/&3(/$ IA

U2( *()&$%,3%12 313#+(;(23 <./%6#+(23( ()3 *( &12)%*<$($ *(/> <+(&3$12) *:<2($@

7%( E

F

+ǫ (3 E

F

− ǫ 8 *( 6(&3(/$ *:12*( k

F

+

~vǫF

(3 k

F

~vǫF

(3 *( ),%2 s (3 − s ./%

3$#6($)(23 +:%23($9#&( ,1/$ *122($ 2#%))#2&( K /2( ,#%$( *( B11,($ *#2) IA V#2) +( ;<3#+ 21$;#+8 12 ,(/3 #+1$) ,#$+($ *( ,#%$() *:?2*$((6 &#$ +() *(/> ,#$3%&/+() - )123 ,$<)(23() (2 ;N;( 3(;,) #6(& /2( &12*%3%12 *( ,'#)( ,#$3%&/+%C$(A W+ 2:-

# #/&/2 ,13(23%(+ #33$#&3%9 (23$( +() *(/> <+(&3$12) &1;;( *#2) +( )/,$#&12*/&@

3(/$8 ;#%) +# &1'<$(2&( *() $<=(>%12) *:?2*$((6 ,($;(3 *:/2( &($3#%2( 9#O12 +# X*%Y/)%12Z *() ,$1,$%<3<) )/,$#&12*/&3$%&() *#2) L [ (Y(3 \(%))2($8 #,,#$%@

3%12 *:/2 7#, *#2) +# *(2)%3< *:<3#3)8 ,$1,#7#3%12 *:/2 &1/$#23 212 *%))%,#3%98

#/7;(23#3%12 *( +# &12*/&3#2&(8 (3&AAA GF]8 F!8 ^_8 ^D8 ^ 8 ^`HA

I% +( &1/$#23 &%$&/+( */ )/,$#&12*/&3(/$ 6($) +( ;<3#+ 21$;#+8 12 # #+1$) +() ;N;() $<=(>%12) *:?2*$((6 (2 $(26($)#23 +( )(2) */ 3(;,)A a2 ,(/3 #+1$)

&12)%*<$($ /2 3$1/ $<3$1*%Y/)< K +:%23($9#&( (2 /2 <+(&3$12 (2 #5)1$5#23 /2( ,#%$(

*( B11,($8 &( ./% ()3 <./%6#+(23 K &12)%*<$($ /2( ,#%$( *( B11,($ 3$#2);%)( *#2) +( ;<3#+ 21$;#+ )1/) 91$;( *( *(/> <+(&3$12) &1$$<+<) (2 ,'#)(A

U2( *()&$%,3%12 3$C) ,$#3%./( */ 3$#2),1$3 K 3$#6($) /2( 012&3%12 IL *(

3$#2),#$(2&( #$5%3$#%$( K <3< 9#%3( ,#$ b+12*($8 c%2d'#; (3 e+#,f%0d Q;1*C+(

bceS G^FHA B( ;1*C+( ,($;(3 *( &#+&/+($ +# ,$15#5%+%3< *( $<=(>%12 ),<&/+#%$(8

*( $<=(>%12 *:?2*$((6 1/ *( 3$#2);%))%12 *( ./#)%,#$3%&/+( (2 912&3%12 *( +:<2($@

7%( *( +:<+(&3$12 %2&%*(23 (3 *( +# 3(2)%12 (23$( L (3 IA a2 ,(/38 #6(& &( ;1*C+(8

*<*/%$( +# &#$#&3<$%)3%./( &1/$#23@3(2)%12 *( +# 5#$$%C$(A V#2) +( ;1*C+( bce8 +( ;<3#+ 21$;#+ ()3 &12)%*<$< &1;;( 5#+%)3%./(8 %+ # *12& /2( $<)%)3#2&( 2/++(

(3 +() <+(&3$12) 2( '(/$3(23 +# 5#$$%C$( ./:/2( 91%)A

(31)

! !"#$%&' () *+, %$+,- *+-'#!-+, !./&$0'-

! ! "#$%&'#$( )*)

"#$%&'(') *+,-. )#$*-. /%, 0.-1+ /),$/ 2/'3 %'0$-1#)2'1,/'$%4 ./% 0-5$/% 2(6)7 2$//8 &'5 ,$-8/$%/), ./ *+,-. 2/ 9-:#) 1#;+$/),/ -<%#$</), 2/% 0-5$/% 2/ =##0/$

> ')/ 5),/$9-1/ 0#'$ ./% ,$-)%*/,,$/ > .(-',$/? =(/%, 2/ 1/,,/ 9-:#) &'(5. 0/', /35%,/$ ') 1#'0.-@/ A#%/0;%#) /),$/ ./% 2/'3 %'0$-1#)2'1,/'$%?

B-)% ') *+,-. 0'$ 1#**/ ./ 1'58$/ &'/ )#'% ',5.5%#)%4 ./ .5<$/ 0-$1#'$%

*#C/) l

p

/%, 2(/)85$#) ! )*4 1/ &'5 /%, <5/) 5)9+$5/'$ -'3 -',$/% .#)@'/'$%

1-$-1,+$5%,5&'/% 2-)% )#% +1;-),5..#)%? "/% +1;-),5..#)% &'/ )#'% +,'25#)% %#), 2#)1 25D'%59%4 /, ')/ 0-$,51'./ 0-$1#'$, /) ') ,/*0% t ')/ 25%,-)1/ *#C/))/ L =

√ Dt %'58-), .(-3/ 2/ .(+1;-),5..#)4 -8/1 D = v

F

l

p

/3 ./ 1#/E15/), 2/ 25D'%5#) 2' *+,-. )#$*-.? "#$%&'(')/ 0-5$/ 2(6)2$//8 ,$-8/$%/ .(+1;-),5..#)4 ./% 2/'3 +./1,$#)% -11'*'./), ')/ 25D+$/)1/ 2/ 0;-%/ F

∆φ = 2ǫ

~ v

F

v

F

t = 2ǫL

2

~ D GH?IJ

"#$%&'/ .- 25D+$/)1/ 2/ 0;-%/ 2/85/), 2/ .(#$2$/ 2/ π4 #) 0/', 1#)%52+$/$ &'/ .- 25D'%5#) 2/% 2/'3 0-$,51'./% %'$ ./% 5*0'$/,+% /%, 2+1#$$+.+/? "- 1#;+$/)1/ 2/

.- 0-5$/ /%, -.#$% 0/$2'/ /, /../ )/ 0/', 0.'% ,$-)%0#$,/$ 2/ 1#'$-), %'0$-1#)7 2'1,/'$? K) 0/', 2+L)5$ .(+)/$@5/ 2/ M;#'./%% &'5 /%, .- @$-)2/'$ 1-$-1,+$5%-), ./% N#)1,5#)% OPO .#)@'/% F

E

T h

= ~ D

L

2

GH?QJ

K) 0/', 8#5$ 1/,,/ &'-),5,+ 1#**/ .- <-)2/ 2(+)/$@5/ -',#'$ 2/ .(+)/$@5/ 2/

R/$*5 2-)% .-&'/../ ./% 0-$,51'./% 0-$,5150/), %5@)5L1-,58/*/), -' 1#'$-), %'7 0$-1#)2'1,/'$?

S) ,/$*/% 2/ 2/)%5,+ 2(+,-,%4 5. -00-$-T, ') @-0 5)2'5, 2-)% ./ *+,-. )#$*-.

2/ .-$@/'$ 3, 12 E

T h

> 25D+$/)1/ 2/ 0;-%/ )'../ /),$/ ./% 2/'3 1#)2/)%-,% %'0$-7 1#)2'1,/'$%? "/% 1#)25,5#)% -'3 .5*5,/% 2+0/)2/), 2/ 1/,,/ 0;-%/ /, .- .-$@/'$

2' 0%/'2#@-0 25*5)'/ .#$%&'/ .- 25D+$/)1/ 2/ 0;-%/ -'@*/),/ 0#'$ %(-))'./$

.#$%&'/ Φ

1

− Φ

2

=

π2

UVV4 HWX?

!" #$%&'() *)+ +,-'./&0*,/1),'+ $23'(*)+

!+!, -./0&'#$( 123(0145

"- 2/%1$50,5#) 1572/%%'% 0/$*/, 2/ 1#*0$/)2$/ .(/D/, 2/ 0$#35*5,+ *-5% )/ 0/$7

*/, -' *5/'3 &'/ 2(/3,$-5$/ 2/% #$2$/% 2/ @$-)2/'$? S) %/ <-%-), %'$ ./ 9#$*-7 .5%*/ 2/ Y/.2C%; 2/% 9#)1,5#)% 2/ Z$//) ;#$% +&'5.5<$/ UVIX4 [%-2/. - 2+$58+ 2/%

+&'-,5#)% 0/$*/,,-), 2/ 2+1$5$/ 1#$$/1,/*/), .(+8#.',5#) 2/ .- %'0$-1#)2'1,585,+

2-)% ./% %C%,\*/% 25D'%59% UVQX? =/ %#), 2/% +&'-,5#)% 25,/% &'-%51.-%%5&'/%4 1(/%,7

>725$/ 0#'$ ./%&'/../% ,#',/% ./% .#)@'/'$% 1-$-1,+$5%,5&'/% %#), ,$\% %'0+$5/'$/%

> .- .#)@'/'$ 2(#)2/ 2/ R/$*5 /, 2#)1 0#'$ ./%&'/../% ./% @$-)2/'$% 0/'8/), ],$/

1#)%52+$+/% 1#**/ .#1-./%? B-)% ./ 1-% ')525*/)%5#))/. /) .(-<%/)1/ 2/ 1;-*0

*-@)+,5&'/4 1/% +&'-,5#)% %(+1$58/), F

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