Andreev Bound States — Topological Junction

Josephson junction Andreev levels and Majorana zero modes at phase difference phi

In an SNS Josephson junction, Andreev reflection creates bound states at energies E_A = ±Delta*sqrt(1-T*sin^2(phi/2)). At phi=pi, E_A->0 for T->1 (perfect transparency). In topological junctions (Kitaev chain), the ABS touches zero at phi=pi due to Majorana fermion parity protection, giving a 4pi-periodic supercurrent.