Real Spin in Pseudospin Quasiparticles of Bilayer Quantum Hall systems

B. Roostaei , H.A. Fertig ,K. Mullen

1)Department of Physics and Astronomy,University of Oklahoma,Norman,OKlahoma,

2)Department of Physics and Astronomy,University of Indiana,Bloomington,Indiana

3)Kavli Institute for theoretical physics,University of California,Santa Barbara,CA

3,1 2 1

Funding :NSF MRSEC DMR-0080054, NSF EPS-9720651 and NSF DMR- 0454699

Outline

• Double layer QH systems as anisotropic Heisenberg magnets .

• charged excitations .

• Experimental observations suggest spin is involved in excitations .

• Including both spin and pseudospin in Hartree-Fock equations .

• Preliminary results .

d

Double layer electron gas in strong magnetic field :

for finite layer separations even in the absence of interlayer tunneling .

Coherence between layers :

1T

Pseudospin formalism :

Anisotropic Heisenberg magnet in long wavelength approximation :

deEmrdrmrdmrdH zxSASE ,142

22

2

eBtSAS /,2

Double layer systems :

Vortex-antivortex excitations called :

Meron-Antimeron = Bimeron

They carry electric charge of 2/e

/01.0,0,1.0/,04.1 2eztd

Pseudospin-z

Motivations from Experiments:

Assumptions : Real spin fluctuations in QH state of double layers are frozen in majority spin band .

D. Terasawa,et. Al.,cond-mat/0403512

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 :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.

All the above 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 SU(4) 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.

Spin Textures (Skyrmions)

Skyrmions are the low energy spin excitations of monolayer QH systems.

Skyrmions are similar to Bimerons by a spin rotation around y-axis.

/01.0,0,1.0/,04.1 2eztd

yy

zx

xz

SS

SS

SS

… Skyrmions

The microscopic wavefunction of a skyrmion is an admixture of spin up and down single particle states with different angular momentum :

01,, 0)(

mmmmm avau

This suggests that we maybe able to get spin-pseudospin textures by allowing the minority state to be an admixture of spin and at the same time symmetric (S) and antisymmetric (A) single particle states.

,

SU(4) formulation :

RLA

RLS

2

12

1

4

3

2

1

,

,,

,

,,

A

AS

S

ASHF will find a linear combination of these states that minimize energy subject to the constraint of being a single Slater determinant.

,

,

,

,

A

A

S

SSkyrmion Bimeron

,

,

,

,

A

A

S

S

Spin-pseudospin textures :

Our goal is to find densities using HF approximation for Green’s function. 4,3,2,1,

)( ,,

qqccq

We look at a lattice of textures.

Texture has a special property.

for example a skyrmion :

90

yx iSSq )(

)()( qeq i

If our densities follow the above it means we have textures.

4

3

2

1

,

,,

,

,,

A

AS

S

AS

/01.0,/07.0

1.0/,08.122 ezet

d

Real spin texture

Excess of the total charge density n(r)-1

/01.0,0

1.0/,08.12ezt

d

Pseudospin texture

Excess of the total charge density n(r)-1

/01.0,01.0

1.0/,08.12ezt

d

4

3

2

1

,

,,

,

,,

A

AS

S

ASyx iSS 12

0 0.04 0.1420

2

7

14

0 0.04 0.14

02

7

14

A

2.0/,04.1 d

0 0.004 0.01 0.014z2

2

4

10

0 0.004 0.01 0.014

2

4

10

A

/01.0 2ez

/006.0

2.0/,08.12et

d

number of electrons in minority spin band and in antisymmetric spin band per quasiparticle v.s. tunneling and Zeeman gap.

HF equations support the excitations with spin flip at finite layer separation and small tunneling.

The observed signatures of low energy spin excitations at QH state in double layer systems could be explained by introducing spin-pseudospin textures supported by HF equations.

We still have a lot to do!

Conclusions :

01.0/,04.1 d0,/01.0 2 tez