SSH Model — Topological Insulator Edge States

SSH Model Physics: The SSH chain alternates between intra-cell hopping t₁ and inter-cell hopping t₂. The Hamiltonian in k-space: H(k) = (t₁+t₂cos k)σₓ + t₂sin k·σᵧ. The topological invariant is the winding number ν = (1/2πi)∮ d/dk [ln det H(k)] dk. When t₂ > t₁: ν=1 (topological phase) → protected zero-energy edge states at both ends. When t₂ < t₁: ν=0 (trivial). The gap closes at t₁=t₂ (topological phase transition). Edge states are exponentially localized and protected by chiral symmetry — they cannot be removed without closing the bulk gap. This is the hallmark of bulk-boundary correspondence.