Attractive electron-electron interaction induced by the dynamical Jahn-Teller effect involving degenerate impurity orbitals: a theory of the impurity enhancement of the superconductive transition temperature in dilute alloys

Abstract

The dynamical Jahn-Teller effect associated with a 3d transition-metal impurity atom substituted in a simple metal is examined theoretically. The impurity atom is assumed to carry an essentially twofold-degenerate partially filled E_g-type electronic level lying close to the Fermi surface of the host metal. These degenerate impurity orbitals are shown to couple dynamically to the lattice through the Jahn-Teller effect. This latter coupling is "seen" by the conduction electrons via the resonant "s-d" interaction. The resulting indirect conduction-electron phonon coupling gives rise to an additional pairing interaction in the second order and involves the impurity orbitals dynamically. Under certain conditions of the impurity-level broadening (Δ) and positioning (δ) relative to the Fermi level, the above mechanism leads to a BCS-type attractive interaction parameter V_e-e given by V_e-e≅C_i[Δ²/(Δ²+δ²)²] [E_J-T/2π²ρ(ε_F)²], where C_i is the fractional concentration of the impurity centers, ρ(ε_F) is the density of states at the Fermi level, and E_JT is the Jahn-Teller stabilization energy. The parameter V_e-e has been estimated numerically for the Al: Fe system and is found to be in reasonable agreement with the experimental values reported in the literature. It appears that the anomalously large impurity enhancement of the superconductive transition temperature observed in certain dilute alloys, such as Fe dissolved in Ti, Zr, and Al up to 1 at.%, may find a semiquantitative explanation in terms of the present mechanism. In deriving the above expression, the approximate procedure of unitary transformation was made use of. All renormalization effects were neglected. Also, the quasimolecular approximation was used in treating the Jahn-Teller effect of the impurity center. The many-impurity effect was treated in the spatial randomphase approximation. Certain group-theoretical arguments were employed to arrive at the mixing matrix elements involved in the determination of the width parameter Δ, appropriate to the present mechanism. The actual calculations have been carried out for the case of a simple-cubic host lattice. However, the treatment holds for all centrosymmetric cubic lattices, the differences showing up only in the form of certain multiplicative form factors.