Theory of Superconducting $T_c$ of doped fullerenes

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.

20 pages, Latex, 4 figures available upon request

References in corpus (2)

• Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I
• Excitons in C_60 studied by Temperature Dependent Optical Second- Harmonic Generation

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