Abstract
An orbitally degenerate two-band Hubbard model is analyzed with the inclusion of the Hund's rule-induced spin-triplet even-parity paired states and their coexistence with magnetic ordering. The so-called statistically consistent Gutzwiller approximation (SGA) has been applied to the case of a square lattice. The superconducting gaps, the magnetic moment and the free energy are analyzed as a function of the Hund's rule coupling strength and the band filling. Also, the influence of the intersite hybridization on the stability of paired phases is discussed. In order to examine the effect of correlations the results are compared with those calculated earlier within the Hartree–Fock (HF) approximation combined with the Bardeen–Cooper–Schrieffer (BCS) approach. Significant differences between the two methods used (HF + BCS versus SGA + real-space pairing) appear in the stability regions of the considered phases. Our results supplement the analysis of this canonical model used widely in the discussions of pure magnetic phases with the detailed elaboration of the stability of the spin-triplet superconducting states and the coexistent magnetic-superconducting states. At the end, we briefly discuss qualitatively the factors that need to be included for a detailed quantitative comparison with the corresponding experimental results.
Highlights
The principal purpose of this paper was to formulate a many-particle method which allows us to investigate the spin-triplet real-space pairing in correlated system with an orbital degeneracy
We have carried out a detailed analysis using the statistically consistent Gutzwiller approximation (SGA) for the two-band degenerate Hubbard model with the spin-triplet superconductivity and itinerant magnetism included, both treated on equal footing
The obtained Hund’s coupling and band-filling dependences of the magnetic moment and the superconducting gap parameters are often similar from the qualitative point of view with those evaluated by means of the HF approximation
Summary
We can say that here we discuss some universal stability conditions of the paired and coexistent magnetic-paired states, as well as provide some basic quantitative characteristics This is because, as we show explicitly below, the order parameters and related other quantities are determined by a minimization of either the ground state or free-energy functional which is obtained by integrating lnZ , where Z is the effective grand-canonical partition function, over the single particle effective band energies. The extension of the present model to the uranium system such as UGe2 would require considering orbitally degenerate and correlated 5f2–5f3 quasi-atomic states due to U and hybridized with the uncorrelated conduction band states This means that we must have minimally a three-orbital system with two partially occupied 5f quasi-atomic states (so the Hund’s rule becomes operative) and at least one extra conduction band. If the spin-triplet pairing is taking place in a single band, the paired states must be of odd parity
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