Impurities, Quantum Interference and Quantum Phase Transitions in s-wave superconductors

TL;DR

This paper investigates how quantum interference among multiple magnetic impurities on an s-wave superconductor surface affects local electronic states, order parameter, and induces quantum phase transitions, revealing robustness and tunability of these phenomena.

Contribution

It provides a detailed analysis of quantum interference effects in impurity structures, showing their impact on LDOS, order parameter, and phase transitions, which was not fully understood before.

Findings

Quantum interference signatures are robust despite order parameter suppression.

Changing impurity distance or scattering strength induces first-order quantum phase transitions.

Transitions can alter spin polarization without necessarily causing a $$-phase shift.

Abstract

We study the effects of quantum interference in impurity structures consisting of two or three magnetic impurities that are located on the surface of an s-wave superconductor. By using a self-consistent Bogoliubov-de Gennes formalism, we show that quantum interference leads to characteristic signatures not only in the local density of states (LDOS), but also in the spatial form of the superconducting order parameter. We demonstrate that the signatures of quantum interference in the LDOS are qualitatively, and to a large extent quantitatively unaffected by the suppression of the superconducting order parameter near impurities, which illustrates the robustness of quantum interference phenomena. Moreover, we show that by changing the interimpurity distance, or the impurities' scattering strength, the s-wave superconductor can be tuned through a series of first order quantum phase transitions in which the spin polarization of its ground state changes. In contrast to the single impurity case, this transition is not necessarily accompanied by a $\pi$-phase shift of the order parameter, and can in certain cases even lead to its enhancement. Our results demonstrate that the superconductor's LDOS, its spin state, and the spatial form of the superconducting order parameter are determined by a subtle interplay between the relative positions of the impurities and their scattering strength.