Effective manipulation of Andreev bound states, zero mode Majorana fermion and Josephson current in a superconductor-normal-superconductor junction on the surface of a topological insulator

We study the effective manipulation of the Andreev bound states (ABS), zero mode Majorana fermion and Josephson current (JC) in a superconductor-normal-superconductor junction on the surface of a topological insulator in unexplored regime of parameters. It is found that the energy of the ABS changes dramatically with the phase difference between both superconductors (SCs) in a certain range of the incident angle of quasiparticles. It is shown that the velocity of Majorana fermion and the JC can be effectively tuned in a wide range of the chemical potential in the normal region (μ_N) and the separation width (L) of the two SCs. In addition, we expose that the critical JC and its product with the normal resistance are, respectively, a quarter and the same to those in a graphene-based Josephson junction. The dependence of the critical JC on the chemical potential in the superconducting region is not monotonous: it increases (decreases) for small (large) μ_N.