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arXiv:1305.2806 · New Journal of Physics

Even-parity spin-triplet pairing by purely repulsive interactions for orbitally degenerate correlated fermions

M. Zegrodnik, Jörg Bünemann, Józef Spałek

Published Mar 3, 2014• 31 citations
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Abstract

We demonstrate the stability of the spin-triplet paired s-wave (with an admixture of extended s-wave) state for the limit of purely repulsive interactions in a degenerate two-band Hubbard model of correlated fermions. The repulsive interactions limit represents an essential extension of our previous analysis (2013 New J. Phys. 15 073050), regarded here as I. We also show that near the half-filling the considered type of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation (SGA) for the case of a square lattice. We suggest that the electron correlations in conjunction with the Hund's rule exchange play the crucial role in stabilizing the real-space spin-triplet superconducting state. A sizable hybridization of the bands suppresses the homogeneous paired state.

DOI
10.1088/1367-2630/16/3/033001

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We demonstrate the stability of the spin-triplet paired s-wave (with an admixture of extended s-wave) state for the limit of purely repulsive interactions in a degenerate two-band Hubbard model of correlated fermions. The repulsive interactions limit represents an essential extension of our previous analysis (2013 New J. Phys. 15 073050), regarded here as I. We also show that near the half-filling the considered type of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation (SGA) for the case of a square lattice. We suggest that the electron correlations in conjunction with the Hund's rule exchange play the crucial role in stabilizing the real-space spin-triplet superconducting state. A sizable hybridization of the bands suppresses the homogeneous paired state.
Universal aspects of the Hund’s rule induced spin-triplet pairing are analysed within the two-band Hubbard model on a square lattice. According to our calculations, this pairing mechanism in conjunction with the correlation effect can result in stability of the paired phase in the so-called purely repulsive interactions regime, in which there is no effectively attractive interaction. Furthermore, even though all of the interaction terms are of intrasite character, the pairing contains both intra- and inter-site components. In effect, the gap parameter has a mixture of s-wave and extended s-wave symmetries. The calculations have been carried out with the use of the Statistically Consistent Gutzwiller Approximation developed by us in recent years.
The intrasite and intersite spin-triplet pairing gaps induced by interband Hund's rule coupling and their correlations are analyzed in the doubly degenerate Hubbard Hamiltonian. To include the effect of correlations, the statistically consistent Gutzwiller approximation is used. In this approach the consistency means that the averages calculated from the self-consistent equations and those determined variationally coincide with each other. Emphasis is put on the solution for which the average particle number is conserved when carrying out the Gutzwiller projection. This method leads to a stable equal-spin paired state in the so-called repulsive interactions limit (U > 3J) in the regime of moderate correlations. The interband hybridization introduces an inequivalence of the bands which, above a critical magnitude, suppresses the paired state due to both the Fermi-wavevector mismatch for the Cooper pair and the interband hopping allowed by the Pauli principle.
We discuss the spin-triplet pairing mechanism induced by the Hund rule ferromagnetic exchange.We include explicitly the eect of interband hybridization and treat the problem by starting from an extended Hubbard model for a doubly degenerate band, making the simplest HartreeFock approximation for the part involving the pairing and the Hubbard interaction.The conditions of stability of various phases are determined as a function of both band lling and microscopic parameters.The phase diagram contains regions of stability of the spin-triplet superconducting phase coexisting with either saturated or non-saturated ferromagnetism.Phase diagrams for the cases of constant density of states and that of square lattice have been provided.The inuence of hybridization on the stability of considered phases, as well as the temperature dependences of magnetic moment and the superconducting gap are also discussed.
We consider the coexistence of the Hund's-rule-exchange induced spin-triplet paired state with the antiferromagnetic ordering by starting from the extended Hubbard model for a doubly degenerate band.We use the density of states appropriate for the square lattice and treat the problem in the HartreeFock approximation.The temperature dependences of the superconducting gaps, the magnetic moment, and the chemical potential are presented.The free energy in the considered phase is evaluated, as well as the corresponding free energies in four additional phases: paramagnetic, ferromagnetic, superconducting of type A and superconducting of type A1 coexisting with ferromagnetism; they occur in the proper range of parameters: band lling n and the interaction parameters U/W and J/W .The low temperature values of the superconducting gaps and staggered magnetic moment are also analyzed as a function of band lling.
An extended Hubbard model for a single band, including Coulomb repulsion and correlated hopping between nearest neighbors, is studied using a generalized mean-field approach. Antiferromagnetism and superconductivity are probed for arbitrary occupation number, near and away from half filling. Binding of pairs in the superconducting state of this purely repulsive model is mediated by the correlated hopping in the form of a covalent-bond configuration, with partial intrasite and intersite pairings. A region of coexistence is conjectured, the superconductivity being suppressed by the saturation of the staggered magnetic moment. Singlet superconducting nonmagnetic states are obtained for the almost-empty- or full-band cases. On the other hand, antiferromagnetism induces mixed s- and p-type superconductivities in the neighborhood of half filling.
Phase boundary between spin singlet and triplet superconductivity in the extended Hubbard model with exchange interaction on a square lattice is calculated within meanfield approximation. Basically, antiferromagnetic exchange interaction J is advantageous for the singlet pairing, while ferromagnetic J prefers the triplet pairing. When off-site interaction V is repulsive, the singlet phase and the triplet phase are separated by normal state in the phase diagram against V and J . If V is effectively attractive, however, the singlet and triplet states can compete against each other. We calculate the phase boundary between singlet and triplet phase for various band filling. It is shown that the triplet phase penetrates rather deeply into antiferromagnetic exchange regime for lower band filling, whereas the penetration of the singlet phase is confined in a narrow range of ferromagnetic exchange regime.