Fractional topological insulators

Topological insulator: 2/3 filling a)
λ
1
Thursday, March 22, 2012
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↑ ↑0.5
↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑
↓ ↓ ↓ ↓ ↓ ↓ 3-fold ↓ ↓ ↓ ↓ ↓ ↓
9-fold
0 10 20
&
lattice momentum
α = A, B and co
0
0 1 2 3 U/V
b)
c)
d)
E/V
0.2
0.1
0
U/V = 0, λ = 0
0 ϖ
γ x
2ϖ
ψ † k,σ := c † k,A,σ ,c
U/V = 0, λ = 1 U/V = 3, λ = 1
γ x
single-particle Ham
H 0 :=
k∈BZ
ψ † k
where the 3-vector
B 0,k := 0,
0 ϖ 2ϖ 0 ϖ γ 2ϖ
x
B 1,k +iB 2,k
B
∋
:= 2t