Enhancement, Reduction and Inversion of Isotope Effects Due to Anharmonic Phonons -Migdal-Eliashberg Theory for Superconductivity-

Abstract

Superconducting transition temperatures of a many-electron system coupled strongly with anharmonic phonons have been studied, to clarify how drastically anharmonicity changes the isotope effect from the harmonic case. The diagonal self-energy of electron as well as the off-diagonal one is determined self-consistently within Migdal's approximation. Typical two types of anharmonicities are studied. The first is a sextic anharmonicity induced by a hard-core repulsion. Isotope shifts become almost zero in this case. When this repulsion is stronger, the shifts are reversed. The second is a small negative quartic anharmonicity in addition to the sextic one, just in the case of a mixture of a hard-core and a soft one. In this case, on the contrary, the shifts are greatly enhanced. Discussion is also given in relation to the observed anomalous isotope effects of newly discovered superconductors. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.