Real Spin in Pseudospin Quasiparticles of Bilayer Quantum Hall systems

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

2. 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 .

3. Double layer electron gas in strong magnetic field : Coherence between layers : for finite layer separations even in the absence of interlayer tunneling . Pseudospin formalism : Anisotropic Heisenberg magnet in long wavelength approximation :

4. Double layer systems : Vortex-antivortex excitations called : Meron-Antimeron = Bimeron They carry electric charge of Pseudospin-z

5. 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 . =density imbalance Motivations from Experiments: D. Terasawa,et. Al.,cond-mat/0403512 Signature of electronic low energy spin excitations in nuclear spin relaxtion rate at QH state . Kumada,et.al.,PRL94,096802(2005)

6. I.B. Spielman,et.al.,PRL94,076803(2005) ... Experiments : Response of to heat and rf pulses. 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.

7. Skyrmions are similar to Bimerons by a spin rotation around y-axis. Spin Textures (Skyrmions) Skyrmions are the low energy spin excitations of monolayer QH systems.

8. This suggests that we maybe able to get spin-pseudospintextures by allowing the minority state to be an admixture of spin and at the same time symmetric (S) and antisymmetric (A) single particle states. Skyrmion Bimeron … Skyrmions The microscopic wavefunction of a skyrmion is an admixture of spin up and down single particle states with different angular momentum : SU(4) formulation : HF will find a linear combination of these states that minimize energy subject to the constraint of being a single Slater determinant.

9. Texture has a special property. for example a skyrmion : If our densities follow the above it means we have textures. Spin-pseudospin textures : Our goal is to find densities using HF approximation for Green’s function. We look at a lattice of textures. Real spin texture Excess of the total charge density n(r)-1

10. Pseudospin texture Excess of the total charge density n(r)-1

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

13. Conclusions : 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!