Theory of Josephson Current on a Magnetically Doped Topological Insulator

Proximity induced superconducting states in the surface of magnetically doped topological insulators can host chiral Majorana modes. We consider a Josephson junction in that system with changing the chemical potential, which drives a topological phase transition in the induced superconducting states as well as a metal-insulator transition in the surface states. The local density of states and the Josephson current are analytically calculated by McMillan's Green's function method in terms of the Andreev reflection coefficient. We show that although the magnitude of the Josephson current is greatly enhanced when the surface state changes from insulating to metallic, its temperature dependence drastically changes at the topological phase transition point, reflecting the appearance of the chiral Majorana modes