Theory of superconducting Tc of doped fullerenes.

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 superconduc-tivity to the strong-coupling polaronic and bipolaronic superconductivity occurs at the BCS coupling constant λ ∼ 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 pho-toemission 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 exci-tations 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.