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Register a new userEffect of disorder on Majorana localization in topological superconductors: a quasiclassical approach
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Two dimensional topological superconductors (TS) host chiral Majorana modes (MMs) localized at the boundaries. In this work, within quasiclassical approximation we study the effect of disorder on the localization length of MMs in two dimensional spin-orbit (SO) coupled superconductors. 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 critical value $tau_c$, the Majorana localization length starts to increase. The critical scattering time depends on the relative magnitudes of the two ingredients behind TS: SO coupling and exchange field. For dominating SO coupling, $tau_c$ is small and vice versa for the dominating exchange field.
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We investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a $p_x pm i p_y$ superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length $ell$ is on the same order as the superconducting coherence length $xi$. In contrast, MZMs can survive stronger disorder for $ell ll xi$ as random variations cancel each other within the length scale of $xi$, while an MZM may survive up to very strong disorder for $ell gg xi$ if it is located in a favorable domain of the given disorder realization.
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