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