Fractional topological insulators

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Time-reversal symmetric Abelian fractional liquids T. Neupert, L. Santos, S. Ryu C. Chamon, and C. Mudry PRB (2011) “ ” ν = 0 FQHE constraints from TRS S ≡ 1 4π K = κ ∆ T Abelian Chern-Simons action dt d 2 x µνρ K ij a i µ ∂ ν a j ρ ∆ −κ κ T = κ, ∆ T = −∆ degeneracy on torus for this subclass # GS = = κ det ∆ T Pf κ ∆ T ∆ = ∆ −κ det T −κ κ ∆ 2 −κ = [integer] 2 ∆ Thursday, March 22, 2012
Lattice realization of time-reversal symmetric fractional <strong>topological</strong> liquids 2 T. Neupert, L. Santos, S. Ryu C. Chamon, and C. Mudry PRB (2011); PRL (2011). i b) 2 copies of flatband models, with opposite chirality for flattened Kane+Mele model spins A i B i i Add interactions H int := U i∈Λ ρ i,↑ ρ i,↓ + V ij∈Λ ρi,↑ ρ j,↑ + ρ i,↓ ρ j,↓ +2λρ i,↑ ρ j,↓ Thursday, March 22, 2012
Page 1 and 2: Fractional topological insulators C
Page 3 and 4: Fractional topological insulators C
Page 5 and 6: Landau flat bands are interesting!
Page 7 and 8: Early flat bands D. Weire and M. F.
Page 9 and 10: Possible flat band energies in the
Page 11 and 12: Can go on and on... Parallel flat b
Page 13 and 14: Are there other ways to get flat ba
Page 15 and 16: Quantum Hall effect w/o Landau leve
Page 17 and 18: a) b) Quantum Hall effect w/o Landa
Page 19 and 20: c) ε/t 1 2 0 − 4π k x 4π 3 √
Page 21 and 22: Add interactions 2 b) A i B i A i B
Page 23 and 24: Chern insulator: exact diagonalizat
Page 25 and 26: Is there a fractional Hall effect?
Page 27 and 28: Thursday, March 22, 2012 Is there a
Page 29: Spin quantum Hall effect - two FQHE
Page 33 and 34: Topological insulator: 1/2 filling
Page 39 and 40: = 0 γ x 3-fold 9-fold 0 10 20 Topo
Page 43 and 44: % !" ! Perspective - bulk vs. edge
Page 49 and 50: Classification of non-interacting s
Page 51 and 52: Classification of non-interacting s
Page 53 and 54: 3D Lattice model 3 orbital model on
Page 55 and 56: 3D Lattice model 3 orbital model on
Page 57 and 58: Non-commuting projected position op

Fractional topological insulators

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