Formation of Cooper pairs between conduction and localized electrons in heavy-fermion superconductors

TL;DR

This paper investigates the formation of $c$-$f$ Cooper pairs in heavy-fermion superconductors using the periodic Anderson model, revealing a fully gapped s-wave phase and exotic pairing states through mean-field analysis.

Contribution

It introduces a theoretical framework for $c$-$f$ pairing in heavy-fermion systems, identifying new pairing phases and their conditions.

Findings

Fully gapped $c$-$f$ pairing phase with anisotropic s-wave symmetry

Existence of Fulde-Ferrell and breached pairing phases

Strong Coulomb repulsion facilitates $f$ band formation near conduction band center

Abstract

Cooper pairing between a conduction electron ($c$ electron) and an $f$ electron, referred to as the "$c$-$f$ pairing," is examined to explain s-wave superconductivity in heavy-fermion systems. We first apply the Schrieffer-Wolff transformation to the periodic Anderson model assuming deep $f$ level and strong Coulomb repulsion. The resulting effective Hamiltonian contains direct and spin-exchange interactions between $c$ and $f$ electrons, which are responsible for the formation of the $c$-$f$ Cooper pairs. The mean-field analysis shows that the fully gapped $c$-$f$ pairing phase with anisotropic s-wave symmetry appears in a large region of the phase diagram. We also find two different types of exotic $c$-$f$ pairing phases, the Fulde-Ferrell and breached pairing phases. The formation of the $c$-$f$ Cooper pairs is attributed to the fact that the strong Coulomb repulsion makes a quasiparticle $f$ band near the center of the conduction band.