Impurity Induced Quantum Phase Transitions and Magnetic Order in Conventional Superconductors: Competition between Bound and Quasiparticle states

TL;DR

This paper investigates how magnetic impurities in conventional superconductors induce bound states and lead to quantum phase transitions, affecting magnetic order and the superconductor's properties through analytical and numerical methods.

Contribution

It provides a detailed analysis of impurity-induced bound states and their role in quantum phase transitions, highlighting the interplay between bound and quasiparticle states in superconductors.

Findings

Quantum phase transitions can be controlled by impurity parameters.

Bound state energies determine the system's ground state.

Discontinuities in the order parameter occur at phase transitions.

Abstract

We theoretically study bound states generated by magnetic impurities within conventional $s$-wave superconductors, both analytically and numerically. In determining the effect of the hybridization of two such bound states on the energy spectrum as a function of magnetic exchange coupling, relative angle of magnetization, and distance between impurities, we find that quantum phase transitions can be modulated by each of these parameters. Accompanying such transitions, there is a change in the preferred spin configuration of the impurities. Although the interaction between the impurity spins is overwhelmingly dominated by the quasiparticle contribution, the ground state of the system is determined by the bound state energies. Self-consistently calculating the superconducting order parameter, we find a discontinuity when the system undergoes a quantum phase transition as indicated by the bound state energies.