Stalking the Exciton Condensate: Exotic Behavior of Electrons Under Extreme Conditions Melinda Kellogg Jim Eisenstein Ian Spielman Loren Pfeiffer Ken.

Stalking the Exciton Condensate: Exotic Behavior of ElectronsUnder Extreme Conditions

Melinda Kellogg

Jim Eisenstein Ian Spielman Loren Pfeiffer Ken West

Everhart LectureMarch 10, 2004

Caltech

Extreme Condition #1:

Reduced Dimensionality

2-dimensional electrons

Two-Dimensional Electrons

Electron motion is constrained to only 2 dimensions

e-e-

e-e-

• At the surfaces of metals

• At the surface of liquid Helium

• AND inside specially engineered semiconductor crystals . . .

Two-dimensional electrons exist:

Crommie et al., Nature 363, 524 (1993)

Ga As

ultra highvacuum

heated cells

high qualityGaAs substrate

Al

AlGaAs

AlGaAs

GaAs100 A

allows for precisionengineering of crystal

layer by layer

AlGaAs AlGaAsGaAs

100 A

Quantum Well

AlGaAs

GaAs

100 A

AlGaAs

Double Quantum Well

Ga

As

e-

e-

e-

e-

e-

e-

e-

Si

energ

y

e-

e-

Bilayer Two-Dimensional Electron System

100 A

e-

e-

e-e-

e- e- e- e-

e-

e-e-

e-

e-

e-e-

e-e-

e-e-e-e-

e-

e-

e-e- e-

e- e- e- e-

e- e-

e-

e-

e-

e-e- e-

e- e- e- e-

e- e-

e-

e-

e-e- e-

e-

e-e- e-

e-

e-

e-

e-e-

e-e-

e-e- e-

e- e- e- e-

e- e-

e-

e-

e-e- e-

e- e-

e-

e-

e-

e-

e-e-

e-

e-e-

e-

e-

e-

e-e-

e-e-

e-

e-

e-

e-

e- e- e- e-e- e-

e- e-

e-e-

e-

e-e-

e-

e-

e-

e-e-

e-e-

e-

e-

e-

e-

e-e- e- e- e- e-e- e-

0.5 mm

1.5 mm

10 mm

Extreme Condition #2:

Extremely Low Temperatures

5o C

15 mK

1 meter

Extreme Condition #3:

Very Large Magnetic Field

13 Tesla

1 meter

voltmeter0

e-vdrift

Hall voltage

B

Lorentz Force: magnetic field

velocityelectric field

)Bv(e

F

Ee

F

E

voltmeter0

e-

e-

e-e-

e-

e-

e-e-

e-

e-

e-e-

e-e-e-

e-

e-

e-

e- e-

e-

e-

e-

e-

Hall voltage

I

B

B

VHall

Bne

IHall V

Quantum Hall Effect

VHall

1n

von Klitzing 1980

2

he

2

he

13

I

I

wave nature of electrons

e- de Broglie wavelength

cyclotronf =

v

m

mh

eB2

fv = 22√ √√ eB

2 v

mh=

1 √ eB2

vm

h=2

√ eB2

vm

h=2√

B3√ 7√

Planck’s constant

6.63 x 10-34 Joule · sec

Brogliede

√ eBh

Pauli Exclusion Principle

≥ h2

x p

Heisenberg Uncertainty Principle

~p pRMS = √ eB2

h2√

1

~ √√

x ~√ eBh

none Landau level eBh x

= 1( )2

“one f illed Landau level”“second Landau level”

eBh( )2 ( )

2

e

VHall

1n

von Klitzing 1980

2

he

2

he

13

I

I

n eB

h

B 2IV

Be

VHall

1n

von Klitzing 1980

2

he

2

he

13

I

I

n eB

h

231

IV

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

? ??

??

??

? ?

?

?? ? ?

?

??

?

Spin½ π2hx=Classical Spin

Quantum Spin

Spin½

=

=

+

+

Spin½

=

=

-

-

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

Pseudospin

e-

e-

e-e-e- e-

e-e-

e- e-

E

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

Superposition

e-

e-

e-e- e-

e-e-

e- e-e-

e- e-e- e-

e- e-

= +–

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

Fluctuations

e-

e-

e-e- e-

e-e-

e- e-e-

e- e-e- e-

e- e-

12

9

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

Fluctuations

e-

e-

e-e- e-

e-e-

e- e-e-

e- e-e- e-

e- e-

147

e- e- e-

e-e-

e-e-

e-e-

e-e-e- e- e-

e-

e-e- e- e-

e-

Fluctuations

e-

e-

e-e- e-

e-e-

e- e-e-

e- e-e- e-

e- e-

10

11

Tunneling

Ian Spielman

V

10

5

0d

I/d

V (

10-6

-1)

-20x10-6

-10 0 10 20Interlayer Bias (V)

= electron

= hole

Another way to look at it…

half-integral spin; electrons, protons, neutrons…

zero or integral spin; photons, pions, Helium-4 atoms, paired fermions, sodium atoms…

e-

e-

e-

e-

e-

e-

e-

e-

Fermions:

Bosons:

obey Pauli exclusion principle

don’t obey Pauli exclusion principle

superfluid helium

superconductor

Bose-Einstein Condensates (BECs)

BEC of sodium atoms

Durfee & Ketterle, Optics Express 2, 299 (1998)

Old-Fashioned Excitons

e-

h

= electron

= hole

Stable Excitons

I

I

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e-

h

e- e-e-e-e-e-e-e-e-e-

e-e-e-e-

e-e-e-e-e-e-e-

e-e-e-e-e-e-

I

I

I

Ivoltmeter

voltmeter0

0

3

2

1

02.01.51.00.50.0

I

I

I

I

20

15

10

5

02.01.51.00.50.0

Exciton BEC?

Magnetic Field (Tesla)

Hal

l Vol

tage

(m

icro

volt

s)

M. Kellogg (2004)

½ fillingper layer

Magnetic Field (Tesla)

Lon

gitu

dina

l Vol

tage

(m

icro

volt

s)

½ fillingper layer

The End

acknowledgements: