Majorana Bound States — Topological Nanowire

Non-Abelian Quasiparticles

A semiconductor nanowire with strong spin-orbit coupling, proximity-coupled to an s-wave superconductor, and subjected to a Zeeman field B can enter a topological phase hosting Majorana zero modes at its ends.

The topological transition occurs when the Zeeman energy exceeds the critical value: VZ > √(Δ² + μ²). In the topological phase, a zero-energy state appears (visible as a peak at E=0 in the tunnel spectrum).

Majorana fermions are their own antiparticles: γ† = γ. They could encode topological qubits immune to local noise — a holy grail of quantum computing.

Kitaev condition: |V_Z| > √(Δ²+μ²)
Topological invariant: Q = sgn(Pf[iH(0)])
γ₁ = (c + c†)/√2, γ₂ = (c − c†)/i√2