We derive an expression for the effective mass of an electron for a multi-band system, starting from a thermodynamic potential expressed in terms of a single-particle Green's function and using an effective equation of motion in the effective mass representation (EMR). We consider a four-band model around G point-one conduction band and three valence bands, for the w-ZnO. We diagonalize the k p ⋅ Hamiltonian, using double-group basis functions for the energy levels, by considering the conduction band and each of the valence bands separately, and obtain the energy dispersions in terms of Luttinger-Kohn parameters. Effects of other bands on each of the valence band energy is considered by going beyond parabolic approximation and adding fourth degree terms in the wave vector to the energy dispersion. The resulting bands' structures agree well with other reported electronic structures. The formalism is then used to calculate the effective masses and effective g-factors at the G point, and as functions of the wave vector. Comparisons with other calculated values and experimental values show reasonably good agreement.
We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron–electron interactions, where the wavefunction is expanded over a complete set of Luttinger–Kohn wavefunctions. We use the Luttinger–Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron–electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.