Interband and kinetic corrections to the electronic Boltzmann transport equation

Abstract: Interband effects such as coherence/tunneling have recently been shown to give an important contribution to the charge and heat transport properties under certain conditions. These can be captured by adding corrective terms to the semiclassical Boltzmann transport equation. In recent derivations of this type of transport equations that are based on the density matrix formalism, there remain, however, certain omissions. These derivations also rely on a particular type of relaxation time approximation and a band-diagonal form of the interaction self-energies. In this work we derive the interband terms of the electronic Boltzmann transport equation starting from the Keldysh formulation of the quantum kinetic equation and considering the band non-diagonality of the electron-impurity and electron-phonon self-energies. We introduce a minimally modified Kadanoff-Baym Ansatz, and find a quantum-corrected, matrix Boltzmann transport equation that is well beyond the current state of the art theory. We show that the occupations and coherences are interdependent, and that the kinetic corrections due to the included interactions cannot, in general, be ignored. This work clarifies the various approximations that must be introduced in an ab initio derivation of Boltzmann-like equations and finds a new matrix Boltzmann transport equation that is suitable for parameters-free numerical implementations.