Strong localization of Majorana end states in chains of magnetic adatoms

TL;DR

This paper models chains of magnetic adatoms on superconductors to explain the strong localization of Majorana end states, revealing a velocity renormalization effect that confines these states on a very small scale.

Contribution

It introduces a minimal analytical model of Anderson impurities on a superconductor to explain Majorana localization, highlighting the role of velocity renormalization.

Findings

Majorana states are strongly localized due to velocity renormalization.

The localization length is much smaller than the superconductor's coherence length.

The phase diagram and subgap spectrum are characterized within the model.

Abstract

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] gives possible evidence for Majorana bound states in chains of magnetic adatoms placed on a superconductor. While many features of the observed end states are naturally interpreted in terms of Majoranas, their strong localization remained puzzling. We consider a linear chain of Anderson impurities on a superconductor as a minimal model and treat it largely analytically within mean-field theory. We explore the phase diagram, the subgap excitation spectrum, and the Majorana wavefunctions. Owing to a strong velocity renormalization, the latter are localized on a scale which is parametrically small compared to the coherence length of the host superconductor.