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Etude theorique des phases de densite inhomogene dans
les systemes a effet Hall quantique
Mark Oliver Goerbig
To cite this version:
Mark Oliver Goerbig. Etude theorique des phases de densite inhomogene dans les systemes a effet
Hall quantique. Matière Condensée [cond-mat]. Université Paris Sud - Paris XI, 2004. Français.
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HAL Id: tel-00007072
https://tel.archives-ouvertes.fr/tel-00007072
Submitted on 8 Oct 2004
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ʛ)% Á v~)%(1u!¹ 9 +%)%„v „u4)%ƒÉ1 =u w = 49! v !4j!„ !
1=)% (v4 Ëdз ®uÁʛ = )%1 })%(1 ]# x ; @ A T ,/X U A W 2wd)N! x A
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v4= )%1H ¾y„4ʛ u&- ÁÁxƒ1&= &v !19ʵ (v4ˆÚ·
=€„v =!1v 9v|?B„ )€É0 Á„ )%ƒ ¿ T')= ƒ)%H 1 ! !?‚!1} ˆ
v4=u ) [ʛ) Á 4·151 5 )%v 4[€#%=_!P1 4 v =u )%4!1P4)%)%+x * Ü w + Ë !0És H)%  } $u}ڜ! = u v51{Îl +%H€#%=1v ! !1 v4=u ) 9 c 4 wœ ! 1œv ! 1 [email protected]? ÑÒ4v ) ' #Á)%! ! „ {}(1!v v4' #1wœH!
„ ¹ !( 1² !0u)%!ƒ-#„ v4! ; @ " W T Â0w7€# = v|?‚u "
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Résistance de Hall
EHQ fractionnaire
[ ν = p/(2sp+1)] 1/3
I
gaz d’électrons 2D
2/5
3/7
4/9
−I
4/11
7/19
10/27
1/2
résistance
longitudinale
4/7
3/5
résistance
de Hall
2/3
EHQ entier
1
[ ν = n]
2
3/8
nouveaux
11/29
états
8/21
5/13
résistance longitudinale
3
5
4
Champ magnétique
Ë !#"$%&"$'()*(+-,/.01234 +'685 7&8'+"-'9:'/;5 "$<)!8'
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c +89BA"$C7Y7+ =?> <B2,eLfgh:
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> 7+7 > 588,
ÂÄ
§™“*Š|‹Ÿ‡0R‘‰ŒŠµ—µ‡Œ“
(a)
(b)
1000
Cristal d’îlots avec M=3
électrons par site
ρxx (Ω)
750
9/2
T=25mK
V
I
V
I
11/2
500
13/2
7/2
5/2
250
0
Phase de rubans
0
...
1
3
2
2
N=1
3
4
5
B (Tesla)
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0 > 'b)< > +Tu'+%F-<B"$'%<+85 )*OB"$'92tG?F-'+‹8'b7 > '():;5 L,
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4 „=v )%1+%4 ! v ¾<x ; @ T  \€ T  \€ à T  \ * + w)%v n !1v4®u )%
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= ] !0É \v !4w!œ ] ! Py v P]  u 4P( 4 _„Pv &ʛ)%
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!1( P)% +„v c É1 P _!n ) n œ=u4# 9nv !4†
з!1 + =)%!1v *‚®Š+ Ë*Õ[)%!1u9= !H )%9( H !1c!t  #%v )%*
1 )%  1„Á4!1{}x m1v { )%v4!1u4)%zu )%!1# !ƒ$#% !1v|?B„ )3É04y„ )%t1= Á¹)Œ @wN!d)%1Á1 = ! Á !1( u„u4! * Ü w + Ë
Ç_ !1Hy 1! 4È ƒvÆ =)%Á1 1 )%lu )% 4! „4È!lv4 l „ v =u )%4!1 ) v 15v 4! 54=)% (v4ËÇm ;-Ñ _ v 5!0É
„ N )%~1!·u) !1u[v4·!0Éz7x vÆP 1!v )%&=) !v )%j( ; v4=u ) ·
)%=)%Ám(„ 7=) Á{!1mv _Ñ Ám Á4v4 )% @w3v/?‚ 1 )€É0 Á„u4)%j ¿ * '5 +Ë
‡Šµ—\¢•1Š|—›‡Œ“²*‘-Š|‹u•¢•„—4–[Ž&‡‰ŒŠµ‹‡Œ‹u•1Š
Â
réentrance de l’EHQE
0.35
a)
EHQE
2
2
Rxy (h/e )
h/3e
7/2
0.30
3+4/5
h/4e
0.25
3.2
2
(EHQF)
3.4
3.6
3.8
4.0
Champ magnétique (Tesla)
P522b)'(<"-'9%‹ €uxu0MgC8)+<+25 u7"-<0Z*8'O2'!V ‘V’n“U” |ˆ;–n,
ËBÃ 800
Rxx (Ohms)
3+1/5
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v/? ==H 7v4c= 77v4 !4P! u !Ë*Ç_Hv4 „4m!19) 4#„„u4)%
&=Hu €# „ [email protected]&400
)= )%u®€Ë
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¿ v4vˆtx v/?Ô )%4¾0 3.2
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4{# )% @4.0
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§™“*Š|‹Ÿ‡0R‘‰ŒŠµ—µ‡Œ“
u) v $ v/?‚Í ¿! ' cv } u != ! &ʛu„=„v HvÆ}=) ! (*ˆ1ˆ 4 u =
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