Post on 05-Feb-2016
description
Quantum Hall Ferromagnets-III
Ramin Abolfath Luis Brey Anton Burkov Rene Cote Jim Eisenstein Herb Fertig Steve Girvin Charles Hanna Tomas Jungwirth Kentaro
Nomura Leo Radzihovksy (Doug) Rajaraman Mark Rasolt Jairo Sinova Kun
Yang
Les Houches June 2006 University of Texas at Austin
Bilayer Excitonic Superfluidity
|
|
|0 = i (| i + ei φ | i )
Spontaneous Interlayer Phase Coherence =Excitonic Superfluidity =
Pseudospin Ferromagnetism
QHF Anisotropy
QHF Action (M=1)Burkov + AHM PRB (2003)
Fluctuating 4-component
Spinor
Bilayer Spin-Pseudospin HamiltonianBurkov + AHM PRB (2003)
Exchange
Jxx = Jyy
Small dLarge d
Hartree
N=2 M=1 (e.g. Bilayer) Anisotropy
S=N/2 state
Uσ,σ
Anisotropy
Jungwirth & AHM PRB ‘00
SU(2) Quantum Hall Ferromagnetism in GaAs
EisensteinXY order
15
10
5
0
-5
-10
Hal
l Vol
tage
1050Magnetic Field
ShayeganIsing Order
Exciton BEC Basics
Excitons – Elementary Excitations of Intrinsic Semiconductors
e-
h
h
e
Valence Band
Conduction Band
Snoke – U. Pittsburgh
Butov – UCSD
Exciton Condensation is
Spontaneous Interband Coherence
n’ = conduction bandn = valence band Order Parameter
Excitonic BEC and Superfluidity?
Quantum Hall Superfluids
Electrons and Holes in the QH Regime
Add magnetic field
Particle-hole transformation
Assemble Bilayer
300
200
100
0Tunn
elin
g C
ondu
ctan
ce
(10-9
-1
)
-5 0 5Interlayer Voltage (mV)Interlayer Voltage
0
Tunn
elin
g ra
te
0
Josephson-like Currents
Wen and Zee, Fogler and Wilczek, Balents and RadzihovskyStern et al., Fertig and Strayley, ….
I = NФ e 2tsin(φ) ??
II
voltmetervoltmeter0
0
Bilayer Counterflow Transport
15
10
5
0
-5
-10
Hal
l Vol
tage
1050Magnetic Field
Electron-hole Pair Current
Exciton Superfluidity
Kellogg and Eisenstein cond-mat/0401521
Hall Angle Not Large σxx 1000
e2/h
Spin Transfer
Nunez+AHM cond-mat/0403710
Solid State Comm. ‘06
Spin-TransferTheory
Spin Transfer Dynamics
Magnetic Anisotropy
External Magnetic Field
Spin-Current Bias
Bilayer PseudoSpin Transfer
(Interlayer Tunneling Theory)
Quantum Hall Bilayer TunnelingAnomaly is Generalized Pseudospin
Transfer Phenomena
Edge Pseudospin Transfer
Transport Orbitals eV
Condensate Orbitals
k = X / l2
Pseudospin Ordered StateConductance
Pseudospin Transfer Theory
10-3
10-2
10-1
100
Zero
-bia
s C
ondu
ctan
ce (
e2 /h)
d/l = 1.5
80
60
40
20
0
Line
wid
th (
V
)
0.30.20.10Temperature (K)
kBT
10
5
00.10
Current-Driven OrderParameter in Antiferromagnets(Applied Quantum Hall
Ferromagnetism)
Current-Modulated Exchange Bias
Nunez et al. cond-mat/0510797 PRB (to appear) Tsoi et al. cond-mat/0606 (submitted)
Quantum Hall Ferromagnets
Thanks for Listening!
Les Houches June 2006 University of Texas at Austin