Theory of Superconducting $T_{c}$ of doped fullerenes

TL;DR

This paper develops a nonadiabatic polaron theory for superconductivity in doped fullerenes, explaining the crossover from weak to strong coupling and accurately predicting $T_c$, isotope effects, and spectral features.

Contribution

It introduces a comprehensive nonadiabatic polaron model that accounts for realistic interactions and explains superconductivity in doped fullerenes, aligning well with experimental observations.

Findings

Superconductivity crossover occurs at coupling constant $\\lambda \sim 1$.

Calculated $T_c$ and isotope effects match experimental data.

Identified key phonon modes and excitons influencing pairing.

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.