Abstract
We consider a hole superconductor described by a Hamiltonian proposed by Hirsch. For a discussion of the isotope effect within this model the influence of lattice vibrations on the hopping interaction is proposed. Both a harmonic interaction as well as an anharmonic approximation are used to calculate the superconducting critical temperature and the isotope effect parameter α in the weak coupling limit. While the harmonic hole-lattice coupling describes the usual isotope effect, increasing anharmonicity of the hole-lattice coupling decreases the isotope effect leading to a situation known in the high-temperature superconducting oxides.
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