Photoemission spectroscopu of the superconducting and normal state for polaronic systems

Abstract

The normal and anomalous one-particle Green's functions are derived for a system with strong electron-phonon coupling. The collapse of the electron band and the phonon vacuum is studied within the mean-field approximation. We derive the angle-resolved photoemission spectrum for such a system of small polarons in the normal and in a BCS-like superconducting state. The polaronic features of the charge carriers are manifest in a superposition of (1) a rather well-defined peak corresponding to the coherent part of the heavily dressed electron in a polaronic state and (2) a broad featureless spectrum which is practically momentum independent. In the limit of strong coupling, such that the polaronic band width is smaller than the characteristic phonon frequency, an oscillatory structure is superposed onto this featureless incoherent background. Upon going from the normal to the superconducting state we predict a shift downwards of the coherent part of the spectrum accompanied by a change in intensity. The shape of the incoherent part is roughly the same in the normal and superconducting states but its intensity is increased in the latter. We compare these predictions with the experimental results of certain high- T c superconducting materials.