Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators

We study theoretically charge transport properties of normal metal (N) / ferromagnet insulator (FI) / superconductor (S) junction and S/FI/S junction formed on the surface of three-dimensional topological insulator (TI), where chiral Majorana mode (CMM) exists at FI/S interface. We find that CMM generated in N/FI/S and S/FI/S junctions are very sensitively controlled by the direction of the magnetization $\mathit{m}$ in FI region. Especially, the current-phase relation of Josephson current in S/FI/S junctions has a phase shift neither 0 nor $\pi$, which can be tuned continuously by the component of $\mathit{m}$ perpendicular to the interface.