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# Loughborough University Institutional Repository

 Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/1153

 Title: Theory of Superconducting Tc of doped fullerenes Authors: Alexandrov, A.S.Kabanov, V.V. Issue Date: 1996 Abstract: We develop the nonadiabatic polaron theory of superconductivity of $M_{x}C_{60}$ taking into account the polaron band narrowing and realistic electron-phonon and Coulomb interactions. We argue that the crossover from the BCS weak-coupling superconductivity to the strong-coupling polaronic and bipolaronic superconductivity occurs at the BCS coupling constant $\lambda\sim 1$ independent of the adiabatic ratio, and there is nothing beyond'' Migdal's theorem except small polarons for any realistic electron-phonon interaction. By the use of the polaronic-type function and the exact'' diagonalization in the truncated Hilbert space of vibrons (phonons'') we calculate the ground state energy and the electron spectral density of the $C_{60}^{-}$ molecule. This allows us to describe the photoemission spectrum of $C_{60}^{-}$ in a wide energy region and determine the electron-phonon interaction. The strongest coupling is found with the high-frequency pinch $A_{g2}$ mode and with the Frenkel exciton. We clarify the crucial role of high-frequency bosonic excitations in doped fullerenes which reduce the bare bandwidth and the Coulomb repulsion allowing the intermediate and low-frequency phonons to couple two small polarons in a Cooper pair. The Eliashberg-type equations are solved for low-frequency phonons. The value of the superconducting $T_{c}$, its pressure dependence and the isotope effect are found to be in a remarkable agreement with the available experimental data. Description: This is a pre-print. URI: https://dspace.lboro.ac.uk/2134/1153 Appears in Collections: Pre-Prints (Physics)

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