Fractional topological insulators

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More early flat bands E. Dagotto, E. Fradkin, and A. Moreo, Phys. Lett. B 172, 383 (1986). Volume 172, number 3,4 PHYSICS L PHYSICS LETTERS B 22 May 1986 a I ~E C2 C-I = C- 2 tx~, Fig. 2. A two-dimensional example showing the position of the variables used in eq. (1). Of the generic form in sites. U 1 represents an on-site coupling while U 2 couples the variables belonging to the same line. i and J. P. Straley, PRB 6, 4086 (1972) j take the values -+1, +2, +3. A related hamiltonian was originally proposed in ref. [8] in the context of <strong>topological</strong> disorder in a tetrahedrally bonded solid. (A similar model was analyzed in ref. [9] in writing the classical path integral version of two-dimensional Ising model). It can be shown that by choosing a special ratio between U 1 and U2, there is a band crossing at zero momentum. By explicit diagonalization in mo- Thursday, March mentum 22, 2012space or using the method presented in ref. I P,: py=o b Motivation was to get Weyl fermions on the lattice, with a single cone E Z I ~-
Possible flat band energies in the Kagome model D. Green, L. Santos, and C. Chamon, PRB 2010 E = −2g E =+2g E =0 Flat very bottom band Flat very top band φ ± =2π n ± φ ± = π (2n ± + 1) Flat middle band φ + + φ − = π (mod 2π) 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: Early flat bands D. Weire and M. F.
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 and 30: Spin quantum Hall effect - two FQHE
Page 31 and 32: Lattice realization of time-reversa
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
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Non-commuting projected position op
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Fractional topological insulators

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