SSH Model — Winding Number & Topological Insulator

Su-Schrieffer-Heeger (SSH) model: alternating hopping t₁ (intracell) and t₂ (intercell). When t₂ > t₁, the winding number W = 1 and protected edge states appear in the gap.

SSH Parameters

Intracell hopping t₁: 1.0 Intercell hopping t₂: 0.5

Winding number W:

W = 0

Trivial phase (t₁ > t₂)

Physics

H(k) = (t₁+t₂cos k)σ_x
+ t₂sin(k) σ_y

d(k) = (t₁+t₂cos k, t₂sin k)
W = (1/2π)∮ dφ

|t₂|>|t₁|: W=1, edge states
|t₁|>|t₂|: W=0, trivial