Quantum Hall Ferromagnets-II

1. Quantum Hall Ferromagnets-II Les Houches June 2006 University of Texas at Austin Ramin Abolfath Luis Brey Anton Burkov Rene Cote Jim Eisenstein Herb Fertig Steve Girvin Charles Hanna Tomas Jungwirth Kentaro Nomura Leo Radzihovksy (Doug) Rajaraman Mark Rasolt Jairo Sinova Kun Yang

2. Skyrmions

3. Skrymion in 2D O(3) Ferromagnet

4. Form Factor QHF Energy Functional Landau Gauge Energy Functional Exchange Interaction

5. Carry Charge !! Quantum Hall Skyrmions Sondhi et al. PRB ‘93

6. Skyrmions in Ground State- II Hartree-Fock Skyrmion WF Symmetric Gauge LLL Wavefunctions Classical # of reversed spins

7. Skyrmions Size n=0 LL K g Fertig et al. PRB ’94 ‘97

8. Skyrmions in Ground State Fertig et al. PRB ’94 Barrett & Tycko PRL ‘95

9. Skyrmion Crystal Brey et al. PRL ‘95

10. Skyrmion Crystal Collective Excitations Larmour k1.5 ~ phonons k1 ~ new Cote et al. PRL ‘97

11. QHF Graphene Nomura cond-mat/06 – Alicea cond-mat/06 – Yang cond-mat/06

12. Graphene Landau Levels Semenoff Haldane Kane Mele Conduction Valence

13. Graphene Quantum Hall Effect xy xx n Novoselov et al. – Manchester – Nature (2005)

14. Zhang et al. – Columbia – cond-mat/0602649 B= 45 Tesla

15. Exchange Integral A(E)  Landau Band SU(4) Ferromagnetism Arovas/Karlhede (1999) – Ezawa (2002)

16. Landau Band Width Interaction Energy Scale QHF Stoner Criterion Fogler & Shklovskii (1995); Maude et al. (2005) AX > 1  QHF

17. Geim Nature (2005)   Golden Rule Vgate Zero Field Conductivity ?

18. Coulomb Scattering I where 2-3

19. Coulomb Scattering II 

20. Self-consistent Screening Das Sarma Ando Screened Exchange

21. Phase Diagram Nomura cond-mat/0603 PRL Manchester   1.5 Columbia   5.0

22. Broken Symmetry SU(N)/(SU(M) x SU(N-M)) coset space 2 (N-M) parameters

23. Graphene Skyrmions - I Graphne Form Factor Yang et al., cond-mat/0605666

24. Graphene Skyrmions – II SU(N)/(SU(M-1) x SU(N-M-1)) coset space 2 (N-M) + 2 (N-1) parameters Skyrm Lattice has N Goldstone modes k1.5 & 2 k1 & k2

25. Next Time: • Skyrmions • QHF Anistropy – Ising or XY • QHF in Graphene • Quantum Hall Superfluids & Pseudo-spin Transfer Torques