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Journal of Physics Condensed Matter

Spin-triplet paired state induced by Hund’s rule coupling and correlations: a fully statistically consistent Gutzwiller approach

Józef Spałek, M. Zegrodnik

Published Oct 4, 2013• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/25/43/435601

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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.
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.
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 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.
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.
In order to numerically study electron correlation effects in multiorbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory+quantum\text{theory}+\text{quantum}theory+quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's coupling is stable in a wide region of the band filling.
Excitonic phases described by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-orbital Hubbard model with the Hund's rule coupling J . Using the variational cluster approximation, we calculate the ground-state energy and order parameters, and show that the Hund's rule coupling always stabilizes the excitonic spin-density- wave state and destabilizes the excitonic charge-density-wave state. The pair coherence lengths calculated in the spin-singlet and spin-triplet states indicate that only the spin-triplet excitons are paired more tightly with increasing J . The single-particle spectrum and density of states are also calculated to clarify the characters of these excitonic density-wave states.