Interplay between charge, magnetic and superconducting order in a Kondo lattice with an attractive Hubbard interaction

TL;DR

This paper explores the complex interactions between superconductivity, charge order, magnetism, and the Kondo effect in a heavy fermion system with an attractive Hubbard interaction, revealing how these phenomena compete or cooperate under various conditions.

Contribution

The study develops a novel NRG framework in Nambu space to analyze the interplay of multiple orders in a Kondo lattice with attractive interactions, including broken spin symmetry solutions.

Findings

Magnetic order lifts degeneracy between CDW and superconductivity at half filling.

Superconductivity and CDWs influence magnetic ordering and Kondo screening.

System can become a half metal in certain parameter regimes.

Abstract

We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between $s$-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the $f$-electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the $f$-electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening.