Quantum Hall Ferromagnets-II

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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
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Skyrmions
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Skrymion in 2D O(3) Ferromagnet
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QHF Energy Functional
Landau Gauge
Energy Functional
Exchange Interaction
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Quantum Hall Skyrmions
Sondhi et al. PRB 93
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Skyrmions in Ground State- II
Hartree-Fock Skyrmion WF
Symmetric Gauge LLL Wavefunctions
Classical of reversed spins
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Skyrmions Size n0 LL
K
g
Fertig et al. PRB 94 97
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Skyrmions in Ground State
Fertig et al. PRB 94 Barrett Tycko PRL 95
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Skyrmion Crystal
Brey et al. PRL 95
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Skyrmion Crystal Collective Excitations
Larmour
k1.5 phonons
k1 new
Cote et al. PRL 97
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QHF Graphene
Nomura cond-mat/06 Alicea cond-mat/06 Yang
cond-mat/06
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Graphene Landau Levels
Semenoff Haldane Kane Mele
Conduction
Valence
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Graphene Quantum Hall Effect
?xy
?xx
n
Novoselov et al. Manchester Nature (2005)
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Zhang et al. Columbia cond-mat/0602649
B 45 Tesla
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SU(4) Ferromagnetism
Arovas/Karlhede (1999) Ezawa (2002)
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QHF Stoner Criterion
Fogler Shklovskii (1995) Maude et al. (2005)
AX gt 1 ? QHF
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Zero Field Conductivity
?
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Coulomb Scattering I
where
2-3
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Coulomb Scattering II
?
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Self-consistent Screening
Das Sarma Ando
Screened Exchange
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Phase Diagram
Nomura cond-mat/0603 PRL
Manchester ? ? 1.5 Columbia ? ? 5.0
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Broken Symmetry
SU(N)/(SU(M) x SU(N-M)) coset space 2 (N-M)
parameters
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Graphene Skyrmions - I
Graphne Form Factor
Yang et al., cond-mat/0605666
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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
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• Next Time
• Skyrmions
• QHF Anistropy Ising or XY
• QHF in Graphene
• Quantum Hall Superfluids Pseudo-spin
  Transfer Torques