1 2 2.1 [1] [2] 2.1 STM [3, 4, 5, 6] 2.1: 2 ( 3 [1] ) [7, 8] [9]( 2.2)
2 2 2.1.1 (extended state) L (2 L 1, O(1), d O(V), V = L d V V 2.1.2 1985 2 e 2 /h 1980 Klitzing
2.1. 3 [7, 8] 2.2 [10] [8] 2.2: (a) (b) [9] [11] [12] [13] 1
4 2 2.2 [9] 2 [6] 2.2 2.2.1 2 k 0 E C (k) =E C C C δk 2, E V (k) = E V + C V δk 2, (δk = k k 0 ) C C = 2mC, C V = 2m V mc,v E g = E V E C E g E g δk 2 E g δk 1 2 E(k) = ± c δk (2.1)
2.2. 5 Maxwell (2.1) c Dirac Dirac Dirac 2.2.2 2 2 2 2 3 Von Neumann-Wigner [14] 2 - k x, k y 2 2 Von Neumann-Wigner Berry [15] 2 2 H 2 H Tr H = 0 2 2 R z R z ir y H =R x σ x + R y σ y + R z σ z = R x + ir y R = R σ (2.2) z H 2 = R 2 E 2, (E 2 2 2 ), R = R 2 x + R 2 y + R 2 z H ±R R = 0 2 R x, R y, R z 3 2 2 k x, k y 1 (k 0 ) k 0 E = ± δk E = ± δk 2 + m 2 m = 0
6 2 (K,K ) [18] [6] 2 [20] [21] (2.2) k R R(k) R(k k A = i R(k) k R(k) R = e iθ R A = A + k θ A C e iγ [15, 16] γ = C dk A k = S ds B k B = rot A γ C [6] 2.3 2.4 2.1, 2.3 2 [1] 2 [4]
2.4. 7 (a) (b) (c) k y 2.3: 2 [6] H = t (c i c j + c j c i ) i j i j 2.3 c i, c j [8, 6] k y k y 2.1 2.3 2.3 1 k y 1 2 2 H 2D = H1D Z (k y) = H1D A (k y) k y k y H1D Z, HA 1D 2.3 1 1 1 2 2.3(b) 2.3(c) 2 k y 1 1 1 1
8 2 2 2.1 1 2.4.1 1 1 H 1D 1 [6] H Γ {H, Γ} = HΓ + ΓH = 0, Γ 2 = 1 Γ : + E ψ ψ Γ = Γ ψ E ( ψ ψ Γ = 0) ψ Γ ψ, ψ 2 Γ 2.3 2
2.4. 9 STM [4] k y 1 H 1D (k y ) 1 1 1 [6] 1 H(k x, k y ) 2 2, H(k x, k y ) = R(k x, k y ) σ 1 ψ = R(k x, k y ) k x ({H(k x, k y ), Γ} = 0), (mod 2π ) 1 [6] π mod 2π π k y γ(k y ) = i dk x R(k x, k y ) R(k x, k y ) = π k x 0 k y γ(k y ) 1 γ(k y ) Zigzag = π k y > 2π 3 0, γ(k y) Armchair = 0 (k y 0) k y 2.4.2 2 (1) (2) [22] [2, 17, 18, 19]
10 2 2.4: n = 0 [22] n = 0 [7] n = 0 n = 0 n 0 [22] n = 0
2.4. 11 STM n = 0 2.4.3 [1], [23] [6] 2.5: ( [6] 2 k y 1
12 2 k y 1 [24] 2.5 2.5 2 d- [6] [25]
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