Incorporation of incompleteness in the k⋅p perturbation theory

The k⋅p perturbation expansion for the energy of a nondegenerate band, familiar from solid-state texts, provides a convenient method for calculating the effective mass of the band in terms of the eigenstates of the system. As such, it would seem particularly useful in fitting the parameters of an empirical tight-binding model. Unfortunately, this expression is incorrect when applied to a model having an incomplete basis. We find that the correct expression may be derived from the usual result if the incompleteness of the basis is properly taken into account. In addition, since degenerate bands are often of interest, we discuss the correct calculation of their curvatures.