SSH Model & Topological Edge States

The SSH model (1979) is the simplest 1D topological insulator — a chain of dimers with alternating hopping amplitudes t₁ (intra-dimer) and t₂ (inter-dimer). The Hamiltonian in k-space is:

H(k) = (t₁ + t₂cos k)σ_x + t₂sin(k)σ_y

The winding number W = (1/2π) ∮ d(arg h(k)) distinguishes two topological phases: W=0 (trivial, t₁>t₂) and W=1 (topological, t₁<t₂). In the topological phase, zero-energy edge states appear at the chain ends, protected by chiral symmetry — they cannot be removed without closing the gap.