Spinfluctuations versus phonons: The case of Heavy‐Fermion superconductivity

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Abstract
Superconductivity of Heavy‐Fermions, with an emphasis on hexagonal UPt3, is investigated microscopically on the basis of the LNCA‐approximation for strongly correlated electrons in a Kondo lattice and of Eliashberg theory for anisotropic singlet and triplet superconducting order. The effective interaction kernel incorporates exchange of spin fluctuations carried by strongly renormalized particle‐hole excitations as well as exchange of phonons generated by the breathing mechanism. Particular care is taken to include realistic anisotropies in band structure and couplings and to expand interaction kernel and order parameter in appropriate Fermi surface harmonics. Separate interactions and corresponding gap equations are used for pseudo‐spin‐singlet and ‐triplet channel, with a restriction to the case of weak spin‐orbit coupling. Our main results include a detailed study of phonon‐ and spin‐fluctuation mechanisms as a possible source for superconductivity and, in combination, their mutual influence and competition. Furthermore, the questions regarding singlet or triplet order, conventional or unconventional symmetry, order parameter zeros and phase transitions between different superconducting states are addressed. We propose a possible scenario of Heavy‐Fermion superconductivity.

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