Interatomic inelastic current

Abstract

In order to identify the location of an inelastic event and to distinguish between situations that are before or after this event, we derive equations for the interatomic inelastic transmission as a perturbation series in the electron-phonon interaction. This series contains both even and odd ordered corrections, and while the even ordered corrections can be thought as a Dyson’s expansion of the interatomic elastic transmission in the electron-phonon self-energy, the odd ordered corrections represent something new. We explicitly derive expressions for the interatomic inelastic transmission up to second order and the 1st order correction represents the lowest order term of this new family of terms. We apply this to three model systems and are able to distinguish between situations before and after the inelastic event as steps in the 2nd order transmission. We also see that when the transmission is evaluated between atoms that are coupled by the electron-phonon interaction, the 1st and 2nd order terms must be added together to form a meaningful transmission. Within the limited scope of the models considered here, the 1st order term appears to be the signature of the inelastic event.