Superconducting pairing of interacting electrons: implications from the two-impurity Anderson model

TL;DR

This paper investigates how non-local superconducting pairing emerges in a two-impurity Anderson model, highlighting the roles of Coulomb interactions and critical spin fluctuations near quantum criticality.

Contribution

It reveals that effective Coulomb interactions, rather than spin fluctuations, primarily drive superconducting pairing, with critical spin fluctuations preventing Fermi liquid formation.

Findings

Superconducting pairing fluctuations are strong at high energies.

Coulomb interactions act as the pairing glue.

Critical spin fluctuations sustain pairing at low energies.

Abstract

We study the non-local superconducting pairing of two interacting Anderson impurities, which has an instability near the quantum critical point from the competition between the Kondo effect and an antiferromagnetic inter-impurity spin exchange interaction. As revealed by the dynamics over the whole energy range, the superconducting pairing fluctuations acquire considerable strength from an energy scale much higher than the characteristic spin fluctuation scale while the low energy behaviors follow those of the staggered spin susceptibility. We argue that the glue to the superconducting pairing is not the spin fluctuations, but rather the effective Coulomb interaction. On the other hand, critical spin fluctuations in the vicinity of quantum criticality are also crucial to a superconducting pairing instability, by preventing a Fermi liquid fixed point being reached to keep the superconducting pairing fluctuations finite at low energies. A superconducting order, to reduce the accumulated entropy carried by the critical degrees of freedom, may arise favorably from this instability.