Capri Spring School 2014 Broken Symmetries and the FQHE in graphene Allan MacDonald The University of Texas at Austin Inti Sodemann (PRL – 2014) Fengcheng Wu Rohit Hegde Yasufumi Araki Thierry Jolicoeur DOS Ordered States – Stoner Instability d Band Width vs. Exchange Energy s DOS E µ QHF- Stoner-Criterion Maude et al. PRB (2005) QHF Stoner-Criterion is Rigorous Additional Degrees-of-Freedom + Bilayer Excitonic Superfluidity | á 〉 |↓〉 Spontaneous Interlayer Phase Coherence = Excitonic Superfluidity = Pseudospin Ferromagnetism |Ψ〉0 = Πi (| á 〉i + ei φ | ↓ 〉i ) Counterflow Drag Eisenstein – Nature (2012) Exciton Superflow – in pictures e T Le TR e B Lh BR e Counterflow Drag Su & AHM Nature Phys. (2008) Neutral Graphene in a Magnetic Field Neutral Graphene in a Magnetic Field Charge Density Wave Neutral Graphene in a Magnetic Field Spin Density Wave Neutral Graphene in a Magnetic Field Spin Hall State SU(4) Generators Wu et al. Surprising FQHE 4/3, 5/3 strong Bolotin et al., Du et al. Nature (2009) Feldman et al. Science (2012) Skrymion in 2D O(3) Ferromagnet Sondhi et. al. PRB 1993 Skyrmions at ν = 1/3 ? Palacios & AHM PRB ‘98 Δ=0.10 Gap/(e2/l) (Qe,Qh)=(0,0) (Qe,Qh)=(1,0) (Qe,Qh)=(1,1) B ≈ 10 Tesla (Qe,Qh)=(2,1) Δ=0.04 Δ(g=0) ≈ 0.01 to 0.02 g=0.06 Coulomb & Short-Range Energy Scales Jung PRB (2009) Kharitonov PRB (2012) Short-Range Interactions Phase Diagrams Two-Component ν = 1/3 SU(4) Generators Wu et al. SO(5) Order Parameter Neutral Graphene vs. Cuprates Exact Diagonalization Bilayer AB stacking A2 B2 A1 B1 π = πx+iπy =perturbation A B N=8 Quantum Hall Ferromagnets = LL (0,1) = layer = spin A B FQHE: Papic and Abanin arXiv:1307.2909 Electronic XY Ferroelectric n=1 n=0 = n=1 = + n=0 = electric dipole moment Capri Spring School 2014 Broken Symmetries and the FQHE in graphene Allan MacDonald The University of Texas at Austin
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