Stability Analysis on Majorana Zero-Energy State in the Superconductor/Topological Insulator/Ferromagnet Insulator Junction

Abstract

Based on the stability theory of differential equation, we investigate the robustness of Majorana zero-energy state (MZS) which is an important candidate for the topological quantum computation. In contrast to the prior studies exploring the stability of MZS by the numerical verification which depends on the special perturbations chosen in the simulation, our treatment is suitable for the arbitrary perturbations, so the results we obtained are reliable which is ensured by the exact mathematical theory of stability analysis. As an example, we demonstrate this by the robustness of MZS in the superconductor/topological insulator/ferromagnet insulator junction; the analytical and numerical results indicate that the MZS is unstable in this system.