Majorana Fermions

Physics: Majorana fermion: γ = γ† (its own antiparticle). Complex fermion c = (γ₁+iγ₂)/2 splits into two Majorana modes. Kitaev chain (2001): 1D p-wave superconductor with Hamiltonian H = −μΣnⱼ − tΣ(c†ⱼcⱼ₊₁+h.c.) + ΔΣ(cⱼcⱼ₊₁+h.c.). Topological phase: |μ| < 2t → Majorana zero modes (MZM) localized at chain ends. Non-local qubit: one qubit in two well-separated MZMs → protected from local noise. Signature: zero-bias conductance peak in NS junction. Kouwenhoven 2012, 2023: InAs nanowire + Al superconductor experiments. Microsoft quantum hardware program uses Majorana qubits. Phase boundary: |μ| = 2t.