Quantum interference between impurities: Creating novel many-body states in s-wave superconductors

We demonstrate that quantum interference of electronic waves that are scattered by multiple magnetic impurities in an s-wave superconductor gives rise to novel bound states. Specifically, we predict that by varying the interimpurity distance or the relative angle between two impurity spins, the states’ quantum numbers, as well as their distinct frequency and spatial dependencies, can be altered. Finally, we show that the superconductor can be driven through multiple quantum phase transitions in which its total spin $〈s_z〉$ changes between $〈s_z〉=0,$ 1/2, and 1.