Quantum Yu-Shiba-Rusinov dimers

TL;DR

This paper investigates the complex behavior of magnetic adatom dimers on superconductors, revealing quantum effects in their phase diagrams and subgap spectra that differ from classical predictions, with implications for quantum spin systems.

Contribution

It introduces a comprehensive quantum theory for Yu-Shiba-Rusinov dimers, accounting for higher spins, anisotropy, and interactions, and compares results with numerical methods.

Findings

Quantum effects persist in large-spin and anisotropic dimers.

Phase diagrams differ significantly from classical spin models.

The approach aligns well with numerical renormalization group results.

Abstract

Magnetic adatoms on a superconducting substrate undergo a quantum phase transition as their exchange coupling to the conduction electrons increases. For quantum spins, this transition is accompanied by screening of the adatom spin. Here, we explore the consequences of this screening for the phase diagrams and subgap excitation spectra of dimers of magnetic adatoms coupled by hybridization of their Yu-Shiba-Rusinov states and spin-spin interactions. We specifically account for higher spins, single-ion anisotropy, Ruderman-Kittel-Kasuya-Yosida coupling, and Dzyaloshinsky-Moriya interactions relevant in transition-metal and rare-earth systems. Our flexible approach based on a zero-bandwidth approximation provides detailed physical insight and is in excellent qualitative agreement with available numerical-renormalization group calculations on monomers and dimers. Remarkably, we find that even in the limit of large impurity spins or strong single-ion anisotropy, the phase diagrams for dimers of quantum spins remain qualitatively distinct from phase diagrams based on classical spins, highlighting the need for a theory of quantum Yu-Shiba-Rusinov dimers.