Anharmonic polaronic model and high-Tc superconductivity

Abstract

An anharmonic polaronic model is considered. The model consists of the electronic subsystem, described within the extended Hubbard model, coupled to anharmonic local phonons. The canonical-variable-displacement Holstein-Lang-Firsov transformation is used for shifting the phononic coordinate system in order to minimize the energy of the phonons. Then, the effective electronic Hamiltonian is obtained by averaging over the ground state of the phononic subsystem. It is shown that anharmonicity introduces two main additional factors as compared with the harmonic case. First, the band-narrowing factor is a less rapidly decaying function of the electron-phonon interaction strength. Second, anharmonicity introduces further renormalization of the on-site and intersite interaction between fermions. Implications for the application of the polaronic model to the high-Tc systems are twofold. Due to the first factor, higher values of the electron-phonon coupling are allowed without making polarons too heavy as compared with the experimental value of the effective mass in these materials. Second, small anharmonically induced renormalizations may or may not favor superconductivity. Combination of these two effects leads generally to the effective electronic Hamiltonian that yields more favorable conditions for superconductivity to occur than in the harmonic case.

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