Isotope-Shift Exponent and the Gap Ratio for d-Wave Pairing within the Phonon Mediated Mechanism

Abstract

An exact analytical expression for the isotope-shift exponent is derived for the d-wave pairing assuming a phonon-mediated interaction. The role of the orthorhombic distortion and second nearest-neighbor hopping on the transition temperature (T c ) and the isotope-shift exponent (α) are studied. The temperature dependence of the gap parameter and the doping dependence of the gap ratio are also investigated. It is found that introduction of second nearest-neighbor hopping increases T c ) as well as the gap ratio while decreases the minimum value of α. The variation of α with doping is qualitatively consistent with the experimental results of high-T c oxide systems.