Nascent Superfluidity in Bilayer Two-Dimensional Electron Systems
description
Transcript of Nascent Superfluidity in Bilayer Two-Dimensional Electron Systems
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Nascent Superfluidity in BilayerTwo-Dimensional Electron Systems
Melinda KelloggJim Eisenstein
Loren PfeifferKen West
April 29, 2004MIT-Harvard
Center for Ultracold Atoms
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AlGaAs AlGaAs
GaAs
100 A
Double Quantum Well
En
erg
y
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Two-Dimensional Electron Gas
|k ||k|U Uk k
EF
EF
2 2
2
kE
m
0.067 em m
conduction bands
valence bands
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Fermi Disk
( ) /
1
1E kTf
e
kx
ky
kF
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drive layer
drag layer
Coulomb Drag
d pqE
dt
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Coulomb Drag without Magnetic Field
6
4
2
0
D
(
)
43210T e m p e r a t u r e ( K e lv in )
xx,
k TB~
k TB~
drag layer
drive layer
2,xx D T
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2D Electrons in a Strong Magnetic Field: Classical Hall Effect
BLorentz force: )( BvEqF
evD F = qvB
F = qE
BqvqE Dy
DDD qvnJ 22
qn
B
J
E
Dx
yxy
2
&
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2D Electrons in a Strong Magnetic Field: Quantum Hall Effect
1
2 cE
xy
1n
von Klitzing 1980
2
he
2
he
13
*c
qB
m
h
m *
2c
212 m 1
2 2ch
1
2 c
3
2 cE 52 cE
Quantization of orbits:
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2D Electrons in a Strong Magnetic Field: Landau Levels
one f illed Landau level
Degeneracy of the Landau levels:
√ eBh≥ h
2 x p
~p pRMS = √ eB2
h2√
1
~ √√
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Degeneracy of the Landau levels:
x ~√ eBh
none Landau level eBh x
= 1( )2
eBh( )2 ( )
2
D
2Dn
D
one f illed Landau levelsecond Landau level1121 1 1
2
2D Electrons in a Strong Magnetic Field: Landau Levels
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2D Electrons in a Strong Magnetic Field: Density of States
Energy
De
nsi
ty o
f Sta
tes
12 c 3
2 c 52 c
xy
1n
von Klitzing 1980
2
he
2
he
13
2Dn
D
22
1xy
D
B B heBn e eeh
eBD
h
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2D Electrons in a Strong Magnetic Field: Localized States Quantum Hall Plateaus
EF
Energy
30
20
10
0
Rx
y(k
)
1.51.00.50.0
Magnetic Field (Tesla)
c2
1
c21
c21
c2
3
c23
c23
c2
5
c
25
De
nsi
ty o
f Sta
tes
c
eBn
hxy
c
B
n e
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Coulomb Drag in a Strong Magnetic Field
Dra
g(
)
Magnetic Field (Tesla)
T = 0.3 K
6
4
2
00.250.200.150.10
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150
100
50
0
Dra
g(
)
6420Magnetic Field (Tesla)
T = 0.3 K
8
Coulomb Drag in a Strong Magnetic Field
= ½
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300
250
200
150
100
50
0
Dra
g (
)
3.53.02.52.01.51.00.50.01/
T = 0.3 K
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Bd
d ~ Bintralayer Coulomb energy ~interlayer Coulomb energy
d >> B
intralayer Coulomb energy >> interlayer Coulomb energy
d
A few timesB
B
Effective Layer Separation: d/B
B22 DeB n
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Dra
g (
)
3.53.02.52.01.51.00.50.01/
1500
1000
500
0
T = 0.3 K
d/B=2.56
d/B=2.16
d/B=1.79
d/B=2.03
d/B=1.93
d/B=1.85
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Coulomb Drag at low d/B and low Temperature
T = 0.03 K
10
5
0
R x
x,D (
k
/)
1.21.11.00.90.8
T-1
d/B=1.60
d/B=1.83
d/B=1.76
d/B=1.72
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Hall Drag at low d/B and low Temperature
T = 0.03 K
20
10
0
R x
y,D (
k
)
1.21.11.00.90.8
T-1
d/B=1.60
d/B=1.83
d/B=1.76
d/B=1.72
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Quantum Phase Transition as d/B is lowered
T = 0.05 K25
20
15
10
5
01.91.81.71.6
8
6
4
2
0
d/B
Rxx
,Da
t T
=1
(k
)y
Rx
x,D
at
T
=1
(k
))
/
layersstrongly-coupled
layersweakly-coupled
M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, PRL 90, 246801 (2003).
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T = 0.05 K
d/B
Rxx
,Da
t T
=1
(k
)
layersstrongly-coupled
layersweakly-coupled
8
6
4
2
0
2.01.81.61.41.2
T = 0.3 K
T = 0.1 K
T = 0.25 K
Quantum Phase Transition as d/B is lowered
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The Nature of the Strongly-Coupled Phase: Correlated Electron Physics
Bob Laughlin, 1983
Bert Halperin, 1983
fractional quantum
Hall effect
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The (1,1,1) State
Xiao-Gang Wen and A. Zeepredict superfluid mode for (1,1,1) state, 1992
bottom layer= 1/2
top layer = 1/2
T = 1
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Equivalence of (1,1,1) state to easy-plane spin-1/2 ferromagnet:
Kun Yang, K. Moon, L. Zheng,A. H. MacDonald, S. M. Girvin,
D. Yoshioka, Shou-Cheng Zhang, 1994
Pseudospin:
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Pseudospin Ferromagnet
and ie 1
2
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TunnelingV
Ian Spielman, 2000
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Pseudospin current:
Superfluid Mode
J
( )sJ r
J
J
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Equivalence of (1,1,1) state to Bose-Einstein Condensate of Excitons
A.H. MacDonald and E.H. Rezayi, 1990A.H. MacDonald, 2001
November, 2002
J
J
ve-
h
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J
Jv
e-
h
Current Channels: Parallel & Counterflow
J
J
parallel channel counterflow channel
J
J
J
J
J
JCoulomb drag
+ =J
J
J
J
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T = 0.03 K
d/B=1.60
T-1
10
5
0
1.21.11.00.90.8
R x
x,D (
k
/)
20
10
0
1.21.11.00.90.8 R
xy,
D (
k
/)
T-1
Coulomb Drag in Strongly-Coupled Phase: Indirect Detection of Counterflow Superfluid Mode
JJ
Jparallel channel counterflow channel
J
J
J
J
JCoulomb drag
_ =
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Counterflow Measurement
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Hall Resistivity in Counterflow Channel
M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, cond-mat/0401521 (2004).
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Longitudinal Resistivity in Counterflow Channel
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Hall Resistivity in Parallel Channel
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Longitudinal Resistivity in Parallel Channel
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Temperature Dependence at νT=1
20
TxxR R e
~ 500 mK
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carry charge ; vorticity 1
Topological Excitations: Meron-Antimeron Pairslow energy topologically stable excitations
T < T , only appear in neutral bound pairsT > T , unbound vortices appear; order is destroyed
KT
KT
e2+- +-
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Possible Sources of Energy Gap
Finite current creates energy gap for the dissociation of meron-antimeron pairs.
Finite tunneling affects binding of meron-antimeron pairs; energy gap for creation of charged meron-antimeron pair.
Disorder creates free merons regardless; energy gap due to hopping energy.
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Conductivity at νT=1
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In Conclusion
higher tunneling samples, watch tunneling’s effect on meron pair binding less disordered samples – may show Kosterlitz-Thouless phase transition
Future:
We have observed very large conductivitiesin the counterflow channel of bilayer two-
dimensional electron systems at νT=1consistent with the Bose-Einstein
condensation of interlayer excitons.