Transcript Slide 1
Pseudospin Vortex-Antivortex States with Interwoven Spin Texture in Double Layer Quantum Hall Systems Bahman Roostaei
1 ,
Jérôme Bourassa
3
H.A. Fertig
2 ,
Kieran Mullen
1 ,
René Côté
3
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
APS March Meeting 2006
Funding :NSF MRSEC DMR-0080054, NSF EPS-9720651 and NSF DMR- 0454699
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.
Double layer electron gas in strong magnetic field : Coherence between layers :
T
L
R
1
spontaneously coherent for finite layer separations even in the absence of interlayer tunneling.
Pseudospin formalism :
Anisotropic Heisenberg magnet in long wavelength approximation :
H
2
E
d r
2 4
SAS
2
d r
m x
SAS
2
t
/
eB
1
d r
m z
2
E e
,
d
Double layer systems : Vortex-antivortex excitations called : Meron-Antimeron = Bimeron They carry electric charge of
e
/ 2
Pseudospin-z
1 .
04 ,
d
/ 0 .
1 ,
t
0
Motivations from Experiments:
I.B. Spielman,et.al.,PRL94,076803(2005)
pulses. 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.
... Experiments :
Assumptions : Real spin fluctuations in QH state of double layers are frozen in majority spin band . Observation of continuous change from Bimeron to Skyrmion behavior from double layer to monolayer .
D. Terasawa,et. Al.,Physica E 22 (2004) 52-55
=density imbalance
Signature of electronic low energy spin excitations in nuclear spin relaxtion rate at QH state .
d
/
B
1 / 2
Kumada,et.al.,PRL94,096802(2005)
Vortex-Antivortex Structure at Low Tunneling
1 .
1
d
/ 0 .
4
SAS
0 .
02
e
2 /
Excess of the total charge density
SAS
2 10 4
e
2 / 10 20 30 40 0.4
0.2
10 20 30 40 0.15
0.1
0.05
Introducing CP3 Skyrmions
The microscopic wavefunction of a skyrmion is an admixture of spin up and down single particle states with different angular momentum :
m=0 1 2 3 …
m
0 (
u m a
,
m
1
v m a
,
m
) 0 m= 1 2 3 …
HF will find a linear combination of these states that minimize energy subject to the constraint of being a single Slater determinant.
Spin-Pseudospin Structure
A
S
Z
SAS A
S
SAS
d
/ 1
Z
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
Spin-Pseudospin Skyrmion Structure S z 0
Real Spin in Right Layer
S z 0.3
Real Spin in Left Layer
0 .
8
SAS
2 10 4 (
e
2
Z
0 .
004 (
e d
/ 1 .
0 2 / ) / ) Excess of the total charge density : n(r)-1 0.25
0.2
0.15
0.1
10 20 30 40
….Spin-Pseudospin Skyrmion Structure
SPIN UP BAND SPIN DOWN BAND 0 .
8
SAS
2 10 4 (
e
2
Z
0 .
004 (
e d
/ 1 .
0 2 / ) / )
….Spin-Pseudospin Skyrmion Structure
SPIN UP BAND S z 0.2
S z 0.2
SPIN DOWN BAND S z 0.05
0 .
8
SAS
2 10 4 (
e
2
Z
0 .
004 (
e d
/ 1 .
0 2 / ) / ) S z 0.05
Polarization and Energy
Hartree-Fock Energy Difference per electron 0 .
8
SAS
2 10 4 (
e
2 / )
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.
SAS
Skyrmion
SAS Z
1 Bimeron CP3 Lattice Meron-Antimeron
Z
0 .
005
e
2 / 1
d
/