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 T/sub c/ 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 i/sub G/ of the crystal point group G, isomorphic to the factor group scrG/T/sub n/ (scrG = space group, T/sub n/ = group of primitive translations). The vertex functions depend on i/sub G/ 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 UPt/sub 3/ 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 authorsmore » to study the k-space symmetry of superconductivity in heavy-fermion metals.« less