Majorana Wire — Kitaev Chain

Topological superconductor: edge Majorana modes, bulk gap, and phase diagram

Kitaev Chain Parameters

H = Σ[−t(c†ᵢcᵢ₊₁+h.c.) − μc†ᵢcᵢ + Δcᵢcᵢ₊₁+h.c.]
Topological: |μ|<2t (w=1)
Trivial: |μ|>2t (w=0)
Phase: —
Bulk gap: —
Edge mode E: —
Kitaev (2001): the 1D p-wave superconductor has two phases separated by |μ|=2t. In the topological phase, zero-energy Majorana modes bind to the wire ends. These modes are their own antiparticles and immune to local perturbations. The winding number w=1 classifies the topological phase (class D symmetry).

Quasiparticle Energy Spectrum

Edge Mode Wavefunction |ψ|²

Phase Diagram (μ/t vs Δ/t)