Electron-phonon interaction in mixed crystals

A theory of electron-optical-phonon interaction in mixed crystals where there are two-mode phonons present is reported. Based on the pseudo-unit-cell approach the free optical-phonon Hamiltonian and the electron-phonon interaction Hamiltonian of mixed polar crystals are obtained. Polaron energy shifts and electron effective masses of some mixed crystals are discussed by the perturbation method. It is found that, although the Frohlich coupling constant of each phonon mode exhibits a nonlinear relation, the sum of the coupling constants of the two modes shows a linear relation with the concentration of the mixed crystal. Our theoretical result supports that the linear interpolation method used to estimate the Frohlich constants and the polaronic correction of the electron effective masses is valid in the weak electron-phonon coupling case.