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A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] givespossible evidence for Majorana bound states in chains of magnetic adatomsplaced on a superconductor. While many features of the observed end states arenaturally interpreted in terms of Majoranas, their strong localization remainedpuzzling. We consider a linear chain of Anderson impurities on a superconductoras a minimal model and treat it largely analytically within mean-field theory.We explore the phase diagram, the subgap excitation spectrum, and the Majoranawavefunctions. Owing to a strong velocity renormalization, the latter arelocalized on a scale which is parametrically small compared to the coherencelength of the host superconductor.

Strong localization of Majorana end states in chains of magnetic adatoms