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

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