Gunnarsson O., Meden V., Schönhammer K.
The electron spectral function is calculated for a model including electron-phonon coupling to Einstein phonons. The spectrum is studied as a function of the electronic bandwidth and the energy epsilon k of the level from which the electron is removed. A cumulant expansion is used for the time-dependent Green's function, and the second- and fourth-order cumulants are studied. This approach is demonstrated to give accurate results for an exactly solvable two-level model with two electronic levels coupling to local phonons. For a one-band, infinite, three-dimensional model the cumulant expansion gives one satellite in the large-bandwidth limit. As the bandwidth is reduced, the spectrum calculated with the fourth-order cumulant develops multiple satellites, if epsilon k is close to the Fermi energy EF, and as the bandwidth becomes small, results similar to the two-level model are obtained. If epsilon k is more than a phonon energy below EF, the spectrum instead shows a very broad peak, due to the decay of the hole into a hole closer to EF and a phonon. If the spin degeneracy of the electrons is taken into account, the broadening due to the decay of a hole into a hole closer to EF and an electron-hole pair becomes important, even if epsilon k is closer to EF than the phonon energy. The validity of Migdal's theorem for A3C60 (A=K, Rb) is discussed. The intersubband electron-phonon coupling is appreciable for A3C60, and it may be argued that the effective bandwidth is large. It is shown that Migdal's theorem is, nevertheless, not valid for A3C60.
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