Nascent Superfluidity in BilayerTwo-Dimensional Electron Systems

Melinda KelloggJim Eisenstein

Loren PfeifferKen West

April 29, 2004MIT-Harvard

Center for Ultracold Atoms

AlGaAs AlGaAs

GaAs

100 A

Double Quantum Well

En

erg

y

Two-Dimensional Electron Gas

|k ||k|U Uk k

EF

EF

2 2

2

kE

m

0.067 em m

conduction bands

valence bands

Fermi Disk

( ) /

1

1E kTf

e

kx

ky

kF

drive layer

drag layer

Coulomb Drag

d pqE

dt

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

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

&

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:

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

~ √√

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

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

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

Coulomb Drag in a Strong Magnetic Field

Dra

g(

)

Magnetic Field (Tesla)

T = 0.3 K

6

4

2

00.250.200.150.10

150

100

50

0

Dra

g(

)

6420Magnetic Field (Tesla)

T = 0.3 K

8

Coulomb Drag in a Strong Magnetic Field

= ½

300

250

200

150

100

50

0

Dra

g (

)

3.53.02.52.01.51.00.50.01/

T = 0.3 K

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

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

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

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

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).

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

The Nature of the Strongly-Coupled Phase: Correlated Electron Physics

Bob Laughlin, 1983

Bert Halperin, 1983

fractional quantum

Hall effect

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

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:

Pseudospin Ferromagnet

and ie 1

2

TunnelingV

Ian Spielman, 2000

Pseudospin current:

Superfluid Mode

J

( )sJ r

J

J

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

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

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

_ =

Counterflow Measurement

Hall Resistivity in Counterflow Channel

M. Kellogg, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, cond-mat/0401521 (2004).

Longitudinal Resistivity in Counterflow Channel

Hall Resistivity in Parallel Channel

Longitudinal Resistivity in Parallel Channel

Temperature Dependence at νT=1

20

TxxR R e

~ 500 mK

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+- +-

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.

Conductivity at νT=1

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.