First-principles scattering with Büttiker probes: The role of self-energies

Abstract

Understanding electronic transport properties is important for designing devices for applications. Many studies rely on the semiclassical Boltzmann approach within the relaxation time approximation. This method delivers a graphic physical picture of the scattering process, but in some cases it lacks full quantum-mechanical effects. Here, we use a non-equilibrium Green's function Korringa-Kohn-Rostoker (KKR) method with phase-breaking scattering via virtual B\"uttiker terminals as a fully quantum mechanical approach to transport phenomena. With this, we assess the validity of the relation of the self-energy $\mathrm{\ensuremath{\Sigma}}$ to the scattering time $\ensuremath{\tau}$, often used in literature in the case of constant relaxation time approximation. We argue that the scattering time does not affect the thermopower in the Boltzmann approach and thus should take no effect either on the thermopower calculated via the Keldysh approach. We find a nearly linear relation for the transmission function ${T}_{S}({E}_{F},\mathrm{\ensuremath{\Sigma}})$ of free electrons and Cu with respect to $\frac{1}{\mathrm{\ensuremath{\Sigma}}}$. However, we find that this is not the case for Pd. We attribute this to neighboring states contributing due to the additional broadening via the self-energy $\mathrm{\ensuremath{\Sigma}}$. These findings suggest that a simple identification of scattering time and self-energy is not sufficient. Finally, we discuss the benefits and limits of the application of the virtual terminal approach.