Coexistence of spin-triplet superconductivity with magnetic ordering in an orbitally degenerate system: Hartree-Fock-BCS approximation revisited

TL;DR

This paper revisits the Hartree-Fock-BCS approximation to analyze the coexistence of spin-triplet superconductivity and magnetic order in a degenerate Hubbard model, revealing phase diagrams with coexisting phases and effects of hybridization.

Contribution

It introduces a comprehensive analysis of coexisting spin-triplet superconductivity and magnetic states within a degenerate Hubbard model using an improved Hartree-Fock-BCS approach.

Findings

Phase diagram with coexisting superconducting and magnetic phases

Influence of inter-site hybridization on phase stability

Temperature dependence of magnetic moments and superconducting gaps

Abstract

The Hund's-rule-exchange induced and coexisting spin-triplet paired and magnetic states are considered within the doubly degenerate Hubbard model with interband hybridization. The Hartree-Fock approximation combined with the Bardeen-Cooper-Schrieffer (BCS) approach is analyzed for the case of square lattice. The calculated phase diagram contains regions of stability of the spin-triplet superconducting phase coexisting with either ferromagnetism or antiferromagnetism, as well as a pure superconducting phase. The influence of the inter-site hybridization on the stability of the considered phases, as well as the temperature dependence of both the magnetic moment and the superconducting gaps, are also discussed. Our approach supplements the well known phase diagrams containing only magnetic phases with the paired triplet states treated on the same footing. We also discuss briefly how to include the spin fluctuations within this model with real space pairing.