Lattice instability and high superconducting transition temperature

Abstract

The high T_c and lattice instability of some A₃B compounds (e.g. V₃Si, Nb₃Sn) have been considered as resulting from fine structure in the bare density of states (Labbe et al. 1967). An alternative explanation is presented which directly connects their high T_c with the shear mode lattice instability. The electronic structure of the A₃B's is such that there is a significant umklapp coupling of electrons near the Fermi surface to low q TA phonons. This leads to enhanced phonon induced e-e attraction as the TA mode goes soft. Estimates show that for reasonable values of the parameters concerned, one can obtain the observed rise, say from T_c(V₃Ge)=6K to T_c(V₃Si)=17K as the TA mode goes completely soft. With the same parameters, good agreement is obtained with the observed pressure dependence of T_c in V₃Ge and the variation of T_c in the system V₃Ge_xSi_1-x(0<or=x<or=1).