stalking the exciton condensate: exotic behavior of electrons under extreme conditions melinda...
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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: