Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors

TL;DR

This paper investigates how magnetic impurity chains on conventional superconductors host Majorana bound states, revealing hybridization effects with Yu-Shiba-Rusinov states and their impact on energy oscillations and localization.

Contribution

It provides a self-consistent analysis of Majorana bound state localization and energy oscillations, highlighting the hybridization with YSR states and deriving a parameter-free localization functional.

Findings

Strong hybridization between MBS and YSR states causes energy oscillations.

MBS localization decreases with magnetic impurity strength, contrary to coherence length behavior.

Energy oscillations increase with impurity strength even with negligible MBS overlap.

Abstract

We study a chain of magnetic impurities on a conventional superconductor with spin-orbit coupling, treating the superconducting order fully self-consistently. We find and quantify strong hybridization between the topological edge Majorana bound states (MBSs) and in-gap Yu-Shiba-Rusinov (YSR) states, which causes increasing energy oscillations as a function of magnetic impurity strength, even when the direct MBS overlap is negligible. By treating the MBS as a topological boundary state, dependent only on the effective mass gap, we arrive at a fully parameter-free functional form of the its localization which decreases with magnetic impurity strength, opposite to the behavior of the superconducting coherence length.