Kitaev Chain — Class D Topological Superconductor

The Kitaev chain H = -tΣ(c†ᵢcᵢ₊₁ + h.c.) − μΣnᵢ + ΔΣ(cᵢcᵢ₊₁ + h.c.) has a topological (class D, ℤ₂) phase for |μ| < 2t. In this phase, each site i hosts two Majorana operators γᵢ = cᵢ + c†ᵢ and δᵢ = i(c†ᵢ − cᵢ); at the sweet point μ=0, Δ=t, unpaired Majoranas γ₁ and δ_N form zero-energy edge modes. The phase boundary is |μ| = 2t; the topological invariant is the Pfaffian sign Q = sgn Pf[H(k=0)·H(k=π)].