SSH Topological Edge States

Su-Schrieffer-Heeger chain with alternating hoppings t₁ (intra-cell) and t₂ (inter-cell). When t₁ < t₂, a topological phase with winding number ν=1 emerges, hosting zero-energy edge states protected by chiral symmetry.

t₁ (intra-cell): 0.40

t₂ (inter-cell): 1.00

N cells: 16

Highlighted state index: 16

Winding number ν:

—

Gap closes at
t₁ = t₂ (phase boundary)

Edge state energy
→ 0 as N → ∞

Physics: The SSH model is the simplest topological insulator. The bulk Hamiltonian H(k) = (t₁ + t₂ cos k)σₓ + (t₂ sin k)σᵧ traces a circle in (dₓ,dᵧ) space as k sweeps the BZ. The winding number ν counts how many times this circle wraps the origin: ν=1 when t₁<t₂ (topological), ν=0 when t₁>t₂ (trivial). Bulk-boundary correspondence guarantees exactly ν pairs of zero-energy edge states on open chains.