Interaction between photons and electrons

By using a path-integral theory, the photoemission spectra of the electron-phonon (e-ph) coupled systems are calculated exactly. The spectral properties of the e-ph coupled systems based on the 1D and 2D Holstein models are systematically studied under various conditions. The electronic band structure is found to be greatly modified by the multiple scattering effect of electron with phonons, so as to produce a spectral evolution from broad Gaussian at band bottom to two-headed Lorentzian near the Fermi energy. This evolution reflects a transition of electronic states from localized incoherent one to the extended coherent one near the Fermi energy. The results qualitatively agree with recent experiments of high resolution ARPES on the Be (0001) surface and Bi2Sr2CaCu2O8.