Derivation of the Linear Optical Conductivity for Electron-phonon Interactions in Solids by Using the Revised Combined Projection Technique

摘要

A revised version of the combined projection technique introduced earlier by the present authors [J. Korean Phys. Soc. 59, 3372 (2011)] is introduecd and is applied to deriving the linear optical conductivity containing the linewidth function for optical transitions of electrons interacting with phonons in solids. The result is shown to satisfy the population criterion which claims that the Fermi distribution functions for electrons and the Planck distribution functions for phonons should be combined in multiplicative forms in the many-body formalism. The main part of the result is further shown to be indentical with that obtained by using the projection-reduction method [Progr. Theor. Phys. 96, 307 (1996)].