Enhancement ofT c in BCS theory extended by interband two-phonon exchange

Band crossing and hybridization effects on superconductivity are investigated within a weak coupling limit of an extended BCS theory. Two-phonon modiated attractive two-band (p−d) interactions induce anisotropic coupled energy gaps, enhancement of the transition temperatureTc, and a material-dependent isotope effect. The individual gap tokBTc ratios deviate from the usual BCS value but their average recovers approximately the usual value. Effects on ultrasonic attenuation and coherence lengths are briefly discussed.