Majorana Zero Modes — Kitaev Chain

Kitaev chain model for topological superconductivity. When |μ| < 2t, zero-energy Majorana modes appear at the chain ends — protected by topology and immune to local perturbations.

Kitaev Parameters

Topological phase:
Trivial

Kitaev Chain

H = −μΣ n_j
− t Σ(c†_j c_{j+1}+h.c.)
+ Δ Σ(c_j c_{j+1}+h.c.)

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

MZM at ends: γ₁=c₁+c†₁
γ₂ = i(c_N − c†_N)
{γ_i,γ_j} = 2δ_{ij}

Legend

■ Majorana zero modes
■ Bulk spectrum
■ Left edge MZM
■ Right edge MZM