Kitaev Chain & Majorana Zero Modes

Kitaev (2001) proposed that a 1D p-wave superconductor H = -t Σ(c†ᵢcᵢ₊₁+h.c.) - μΣnᵢ + Δ Σ(cᵢcᵢ₊₁+h.c.) hosts Majorana zero modes at its ends when |μ| < 2t (topological phase). Each Majorana γ = γ† is half a fermion: c = (γ₁+iγ₂)/2. The zero-energy edge modes are exponentially localized and are their own antiparticle. This is the simplest model of a topological superconductor (class D, Z₂ invariant). Majorana modes are non-Abelian anyons — a potential platform for fault-tolerant quantum computing.