Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire

TL;DR

This paper investigates how magnetic impurities near the boundary of a superconducting nanowire influence subgap states and magnetic configurations, revealing boundary-induced quantum phase transitions and impurity interaction effects.

Contribution

It provides a theoretical analysis of boundary effects on Yu-Shiba-Rusinov states and impurity magnetic ordering, including analytical and numerical results for various impurity couplings.

Findings

Boundary proximity causes multiple quantum phase transitions.

Impurity magnetic states depend on boundary distance, not just inter-impurity distance.

Analytical and numerical methods agree on impurity ground states.

Abstract

We theoretically study the spectrum induced by one and two magnetic impurities near the boundary of a one-dimensional nanowire in proximity to a conventional $s$-wave superconductor and extract the ground state magnetic configuration. We show that the energies of the subgap states, supported by the magnetic impurities, are strongly affected by the boundary for distances less than the superconducting coherence length. In particular, when the impurity is moved towards the boundary, multiple quantum phase transitions periodically occur in which the parity of the superconducting condensate oscillates between even and odd. We find that the magnetic ground state configuration of two magnetic impurities depends not only on the distance between them but also explicitly on their distance away from the boundary of the nanowire. As a consequence, the magnetic ground state can switch from ferromagnetic to antiferromagnetic while keeping the inter-impurity distance unaltered by simultaneously moving both impurities away from the boundary. The ground state magnetic configuration of two impurities is found analytically in the weak coupling regime and exactly for an arbitrary impurity coupling strength using numerical tight-binding simulations.