Collective Yu-Shiba-Rusinov states in magnetic clusters at superconducting surfaces

TL;DR

This paper investigates collective Yu-Shiba-Rusinov states in magnetic clusters on superconducting surfaces, revealing stable, spin-unpolarized subgap states that are detectable and independent of cluster spin configurations.

Contribution

It analytically characterizes collective YSR states in magnetic clusters, highlighting the stability and detection of spin-unpolarized states regardless of magnetic configuration.

Findings

Spin-unpolarized YSR states are effectively independent of cluster spin configuration.

These states are stable against thermal fluctuations.

Detectable via scanning tunneling microscopy.

Abstract

We study the properties of collective Yu-Shiba-Rusinov (YSR) states generated by multiple magnetic adatoms (clusters) placed on the surface of a superconductor. For magnetic clusters with equal distances between their constituents, we demonstrate the formation of effectively spin-unpolarized YSR states with subgap energies independent of the spin configuration of the magnetic impurities. We solve the problem analytically for arbitrary spin structure and analyze both spin-polarized (dispersive energy levels) and spin-unpolarized (pinned energy levels) solutions. While the energies of the spin-polarized solutions can be characterized solely by the net magnetic moment of the cluster, the wave functions of the spin-unpolarized solutions effectively decouple from it. This decoupling makes them stable against thermal fluctuation and detectable in scanning tunneling microscopy experiments.