Robustness of majorana zero-energy state

Abstract

Based on the principle of linearized stability proposed by Lyapunov, we investigate the robustness of Majorana zero-energy state (MZES), which plays an important role in topological quantum computation. We show that the MZES is not robust enough against the external perturbations, because mathematically it is critically stable instead of being asymptotically stable, and only the states with asymptotic stability can be regarded as robust, therefore, the MZES cannot be used to carry quantum information in topological quantum computation. Our study is different from previous works that usually make the numerical tests by some special perturbations, whereas our analytical derivation is suitable for arbitrary perturbations. As an example, we demonstrate this by the stability analysis of MZES in the spin-orbit-coupled semiconductor/superconductor junction.