effect of density gradients on magnetotransport of quantum hall systems
DESCRIPTION
Effect of density gradients on magnetotransport of quantum Hall systems. L. Ponomarenko. Participants:. Anne de Visser and Dennis de Lang A. Pruisken (ITF, UvA) G. Galeev (IRE, Moscow) H. Kunzel (HHIN, Berlin). Outline:. Introduction Quantum Hall Effect Quantum Critical Point - PowerPoint PPT PresentationTRANSCRIPT
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Effect of density gradients on Effect of density gradients on magnetotransport magnetotransport
of quantum Hall systemsof quantum Hall systems
L. Ponomarenko
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Participants:Participants:
Anne de Visser and Dennis de Lang
A. Pruisken (ITF, UvA)
G. Galeev (IRE, Moscow)
H. Kunzel (HHIN, Berlin)
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Outline:Outline:
Introduction– Quantum Hall Effect– Quantum Critical Point– Motivation
Results– Experiment– Explanation
Outlook
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IntroductionIntroduction
Two-dimensional electron gas (2DEG)– applications:
• high frequency devices
– fundamental research:• Quantum Hall Effect• Weak localization problem
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0 1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
1.0
i = 6
i = 5
i = 4
T = 60 mK
xx (
k)
B (T)
0
2
4
6
xy (k
)
Quantum Hall EffectQuantum Hall Effect
Vxx
Vxy2ie
hxy
22xyxx
ijij
hiexy /2
0xx
0xx 0xx
0xx
0xx
0xx
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Band StructureBand Structure
E
DOS
EF
EE
DOSDOS
EF
EF
B 0
*m
eBE
B = 0
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Effect of Disorder (T = 0)Effect of Disorder (T = 0)
Order
Disorder
E
E
DOS
DOS
E
E
X
X
Filling factor:
eB
nh
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Quantum Phase TransitionQuantum Phase Transition
Takes place at T = 0Critical behavior
– Localization length
For non-interacting electrons
cBB~
3
7
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ExperimentExperiment
1 2 3 4 50
2
4
6
1.80 K 1.05 K 0.45 K 0.189 K
xx (
k)
B (T)
0
10
20
30
xy (
k)
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CriticalityCriticality
InGaAs/InP (H.P.Wei et al., PRL, 1988)
– half width of xx scales as
– maximum slope of xy scales as
= 0.42
Localization length exponent and critical exponent :
TB ~
TB
MAX
xy ~
2,3
7
,2
p
p
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However…However…
AlGaAs/GaAs– S.Koch et al. (PRB, 1991):
ranges from 0.36 to 0.81
– H.P.Wei et al. (PRB, 1992):
scaling only below 0.2 K
Semicircle relation
0.0
0.5
n+1n
xx
(e2 /h
)
xy (e
2/h)
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Introduction (Summary):Introduction (Summary):
Transition between two plateaus is a quantum phase transition
Critical exponent is not universal
Experimental data do not obey
“semicircle” law
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-8 -6 -4 -2 0 2 4 6 80.0
0.5
1.0
1.5
2.0
2.5 Vxx
Vxx
T = 400 mK
GaAs/AlGaAs quantum well
Field (T)
xx (
k)
Different contacts and field polarityDifferent contacts and field polarity
Antisymmetry:
1 2
3 4
5 6
)(BRxx )( BRxx
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0 2 4 6 80
5
10
15
B/B
(%
)
filling factor
Field (T)
xy (
k)
2 3 4 5 60
1
2
Hall ResistanceHall Resistance
Same for both field polarities, but PP transitions on different contacts take place at different fields
1 2
3 4
5 6
Vxy Vxy
)()( BRBR xyxy
)()( BRBR xyxy
)(BRxy )(BRxy
eB
nh
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Antisymmetry results from Antisymmetry results from density gradient !density gradient !
)()(
)()(
DBCA
DCBA
VVVV
VVVV
A
B D
C
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Antisymmetry results from Antisymmetry results from density gradient !density gradient !
A
B D
C
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How to obtain correct data?How to obtain correct data?
Illumination
Averaging data from different contacts and for both field polarities
4.5 4.6 4.7 4.8 4.90.0
0.2
0.4
0.6
B-
B+
after illuminationT = 189 mK
Rxx
(k
)
Field (T)4.5 4.6 4.7 4.8 4.9
0.0
0.2
0.4
0.6
B-
B+
after illuminationT = 189 mK
Rxx
(k
)
Field (T)4.5 4.6 4.7 4.8 4.9
0.0
0.2
0.4
0.6after illumination
T = 189 mK
Rxy (k
)
Rxx
(k
)
Field (T)
4.0
4.4
4.8
5.2
4.5 4.6 4.7 4.8 4.90.0
0.2
0.4
0.6after illumination
T = 189 mK
Rxy (k
)
Rxx
(k
)
Field (T)
4.0
4.4
4.8
5.2
Gradient is 0.25 %
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Recovered semicircleRecovered semicircle
By proper averaging a “semicircle” behavior can be obtained from slightly inhomogeneous sample
5 60.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)5 6
0.0
0.5
xx (
e2 /h)
xy
(e2/h)
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SummarySummary
Antisymmetry effectExplained by density gradientCriterion for sample selection and
reliable temperature rangeSemicircle recovered
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OutlookOutlook
Reliable scaling experiment on plateau-plateau transition
Plateau-insulator transition
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OutlookOutlook
0 5 10 15 200
50
100
150
200
250 T = 370 mK T = 615 mK T = 1.2 K T = 1.9 K T = 2.9 K T = 4.2 K
17.23
R
xx (
k)
B (T)
0
10
20
30
40
B-
B+
Rxy (k
)