Phonon Anomalies and Superconductivity in Transition-Metal Compounds

We present a physically simple but general argument that explains the phonon anomalies and their interrelation to high $T_c\text{'}\mathrm{s}$ in transition-metal compounds. It is shown that covalent-bond formation due to hybridization of metal $d \left(T_{2g}\right)$ states and nonmetal $p$ states near $E_F$ leads to a resonancelike increase of the nonlocal dielectric function. This anomalous increase of the screening produces the phonon softening and explains the interrelation with the high $T_c\text{'}\mathrm{s}$ as resulting from a simultaneous increase of the electron-phonon matrix elements and a decrease in the phonon energies.