Kitaev Chain: Majorana Nanowire

Kitaev Chain is a 1D model of spinless p-wave superconductor. Hamiltonian: H = −t Σ(c†ᵢcᵢ₊₁+h.c.) − μΣnᵢ + Δ Σ(cᵢcᵢ₊₁+h.c.). In the topological phase (|μ|<2t), unpaired Majorana fermions appear at the chain ends — zero-energy modes protected by particle-hole symmetry. These are candidates for fault-tolerant topological qubits. The spectrum shows a gap closing at the phase transition |μ|=2t. Shown: BdG eigenspectrum (blue) with near-zero Majorana modes (teal dots) and spatial wavefunction.