Effect of disorder on Majorana localization in topological superconductors : A quasiclassical approach

Abstract

Two-dimensional (2D) topological superconductors (TS) host chiral Majorana modes (MMs) localized at the boundaries. In this work, we study the effect of disorder on the localization length of MMs in two-dimensional spin-orbit (SO) coupled superconductors within quasiclassical approximation. We find nonmonotonic behavior of the Majorana localization length as a function of disorder strength. At weak disorder, the Majorana localization length decreases with an increasing disorder strength. Decreasing the disorder scattering time below a crossover value τc, the Majorana localization length starts to increase. The crossover scattering time depends on the relative magnitudes of the two ingredients behind TS: SO coupling and exchange field. For dominating SO coupling, τc is small, and vice versa for the dominating exchange field.