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