Possible Pairing Symmetry of Three - dimensional Superconductor UPt 3 — Analysis Based on a Microscopic Calculation —

Stimulated by the anomalous superconducting properties of UPt3, we investigate the pairing symmetry and the transition temperature in the two-dimensional(2D) and threedimensional(3D) hexagonal Hubbard model. We solve the Éliashberg equation using the third order perturbation theory with respect to the on-site repulsion U . As results of the 2D calculation, we obtain distinct two types of stable spin-triplet pairing states. One is the f -wave(B1) pairing around n = 1.2 and in a small U region, which is caused by the ferromagnetic fluctuation. Then, the other is the px(or py)-wave(E1) pairing in large U region far from the half-filling (n = 1) which is caused by the vertex corrections only. However, we find that the former f -wave pairing is destroyed by introduced 3D dispersion. This is because the 3D dispersion breaks the favorable structures for the f -wave pairing such as the van Hove singularities and the small pocket structures. Thus, we conclude that the ferromagnetic fluctuation mediated spin-triplet state can not explain the superconductivity of UPt3. We also study the case of the pairing symmetry with a polar gap. This pz-wave(A1) is stabilized by the large hopping integral along c-axis tz . It is nearly degenerate with the suppressed px(or py)-wave(E1) in the best fitting parameter region to UPt3 (1.3 ≤ tz ≤ 1.5). These two p-wave pairing states exist in the region far from the half-filling, in which the vertex correction terms play crucial roles like the case in Sr2RuO4.