Majorana Zero Modes — Kitaev Chain

Kitaev chain: 1D topological superconductor. When |μ| < 2t, the system is in a topological phase hosting Majorana zero modes at the chain ends.

Kitaev Chain

Chemical pot. μ/t 0.00

Pairing Δ/t 1.00

Chain length N 40

TOPOLOGICAL PHASE

Gap: —

E₀ (MZM): —

H = −t Σ(c†ᵢcᵢ₊₁+h.c.) − μ Σnᵢ + Δ Σ(cᵢcᵢ₊₁+h.c.)

Topological phase: |μ| < 2t
Trivial phase: |μ| > 2t

At |μ|=2t: gap closes — phase transition. In topological phase, Majorana fermions γ=γ† appear at chain ends with E=0.