Eur. Phys. J. B (2017) 90: 44
https://doi.org/10.1140/epjb/e2017-70596-7

Regular Article

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Department of Physics, Faculty of Science, Urmia University, P.O. Box: 165, Urmia, Iran

^a e-mail: h.goudarzi@urmia.ac.ir

Received: 6 October 2016
Received in final form: 22 November 2016
Published online: 13 March 2017

Abstract

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m_zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m_zfs. The superconducting effective gap is renormalized by a factor η(m_zfs), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m_zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m_zfs, the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.