Cooper-pair states for heavy fermions in the atomic representation: UPt3

Abstract

The vertex equation for Cooper pairs of even or odd parity is developed in the Wannier representation taking into account the spin-orbit interaction of the periodic potential. We assume tightly bound d and f electrons and a short-range electron-electron interaction. The eigenvalue equation for the transition temperature Tc is reduced to a small set of coupled integral equations for the vertex eigenfunctions. These functions transform according to one and the same irreducible representation iG of the crystal point group G, isomorphic to the factor group scrG/Tn (scrG=space group, Tn=group of primitive translations). The vertex functions depend on iG and on the distance d between the two mates. The general symmetrization procedure is developed for the vertex function in the atomic representation or, equivalently, for the Cooper-pair orbitals. The application to the 5f orbitals of UPt3 is presented for the contact pairs, the nearest-neighbor and the next-nearest-neighbor pairs. For all configurations, there are even- and odd-parity states by virtue of the inversion center between two U atoms in the nonsymmorphic lattice. The connection is established between the pair functions in the atomic representation and the Bloch representation used by other authors to study the k-space symmetry of superconductivity in heavy-fermion metals. Thereby it is found that —in contrast to the3 k dependence of the vertex functions is governed by the band structure and the periodic spin-orbit coupling.

Source-reported materials — not catalogue approval

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