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

Kun-Hua Zhang a, Zhen-Gang Zhu a,b,∗,1, Zheng-Chuan Wang a, Qing-Rong Zheng a,∗, Gang Su a,∗ a

Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China b School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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 (μN ) 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) μN .