bahman roostaei , jérôme bourassa h.a. fertig , kieran mullen , rené côté
DESCRIPTION
Pseudospin Vortex-Antivortex States with Interwoven Spin Texture in Double Layer Quantum Hall Systems. Bahman Roostaei , Jérôme Bourassa H.A. Fertig , Kieran Mullen , René Côté 1)Department of Physics and Astronomy,University of Oklahoma,Norman,Oklahoma, - PowerPoint PPT PresentationTRANSCRIPT
Pseudospin Vortex-Antivortex States with Interwoven Spin Texture in Double Layer
Quantum Hall Systems
Bahman Roostaei , Jérôme BourassaH.A. Fertig , Kieran Mullen, René Côté
1)Department of Physics and Astronomy,University of Oklahoma,Norman,Oklahoma,
2)Department of Physics and Astronomy,University of Indiana,Bloomington,Indiana
3) Dép. de physique, Université de Sherbrooke
Funding :NSF MRSEC DMR-0080054, NSF EPS-9720651 and NSF DMR- 0454699
1 3
2 1 3
APS March Meeting 2006
Outline
Excitations of Double layer QH systems.
Experimental observations suggest spin is involved in excitations .
Vortex-Antivortex Structure at low tunneling
Including both spin and pseudospin in Hartree-Fock equations .
Existence of spin-pseudospin (CP3) Skyrmion solution at large layer separation.
Polarization and Energy.
d
Double layer electron gas in strong magnetic field :
spontaneously coherent for finite layer separations even in the absence of interlayer tunneling.
Coherence between layers :
1 RLT
Pseudospin formalism :
Anisotropic Heisenberg magnet in long wavelength approximation :
deEmrdrmrdmrdH zxSASE ,142
22
2
eB
tSAS
/
2
Double layer systems :
Vortex-antivortex excitations called :
Meron-Antimeron = Bimeron
They carry electric charge of 2/e
0,1.0/,04.1 td
Pseudospin-z
I.B. Spielman,et.al.,PRL94,076803(2005)
Response of to heat and rf pulses.
xxR
Sensitivity of nuclear spin relaxation time to QH state.
experiments can be understood if we consider excitations at QH phase of double layer contains “real” spin so that this system can have zero energy spin excitations.
suggestions have been made for CP3 spin-pseudospin excitations. Hartree-Fock allows us to look at this idea quantitatively.
S. Ghosh and R. Rajaraman, Phys. Rev. B63, 035304 (2001); Z.F. Izawa and G. Tsitsishvili, cond-mat/0311406.
Motivations from Experiments:
Assumptions : Real spin fluctuations in QH state of double layers are frozen in majority spin band .
D. Terasawa,et. Al.,Physica E 22 (2004) 52-55
Observation of continuous change from Bimeron to Skyrmion behavior from double layer to monolayer .
Kumada,et.al.,PRL94,096802(2005)
Signature of electronic low energy spin excitations in nuclear spin relaxtion rate at QH state .
2/1/ Bd
=density imbalance
... Experiments :
Vortex-Antivortex Structure at Low Tunneling
1020
30
40
1020
30
40
0.2
0.4
1020
30
40
/02.0 2eSAS
1020
30
40
1020
30
40
0.050.10.15
1020
30
40
/102 24eSAS
Excess of the total charge density
Bim
eron
Lat
tice
Mer
on-A
ntim
eron
Lat
tice
4.0/
1.1
d
Introducing CP3 Skyrmions
The microscopic wavefunction of a skyrmion is an admixture of spin up and down single particle states with different angular momentum :
0,1, 0)(
mmmmm avau
HF will find a linear combination of these states that minimize energy subject to the constraint of being a single Slater determinant.
m= 1 2 3 …
m=0 1 2 3 …
A
S
S
A
SAS
ZZSAS
1/ d
Spin-Pseudospin Structure Real spin :
Left Layer : V – A Lattice
Right Layer : A – V Lattice
Pseudo – spin :
Up Spin Band : V – A Lattice
Down Spin Band : A – V Lattice
Sz0.3
Sz0
Real Spin in Left Layer
Real Spin in Right Layer
0.1/
)/(004.0
)/(102
8.0
2
24
d
e
e
Z
SAS
Spin-Pseudospin Skyrmion Structure
Excess of the total charge density : n(r)-1
1020
30
40
1020
30
40
0.10.150.20.25
1020
30
40
0.1/
)/(004.0
)/(102
8.0
2
24
d
e
e
Z
SAS
….Spin-Pseudospin Skyrmion Structure
SPIN UP BAND
SPIN DOWN BAND
0.1/
)/(004.0
)/(102
8.0
2
24
d
e
e
Z
SAS
….Spin-Pseudospin Skyrmion Structure
Sz0.2
Sz0.2
SPIN UP BAND
SPIN DOWN BAND
Sz0.05
Sz0.05
Polarization and Energy
)/(102
8.024 eSAS
Hartree-Fock Energy Difference per electron
Conclusion
HF equations support the spin-pseudospin excitations at large layer separations and small tunneling.
These excitations are combination of spin and pseudospin vortex-antivortex lattices.
The observed signatures of low energy spin excitations at QH state in double layer systems could be explained by taking into account spin-pseudospin textures.
/005.0 2eZ
SAS
Meron-Antimeron
/d
CP3 Lattice
1
Bimeron
CP3 Bimeron
Skyrmion
1
Z
SAS