A method is developed for eliminating spurious solutions from eight-band $\mathbf{k}\cdot \mathbf{p}$ theory. It reduces the bulk dispersion to a cubic equation (quadratic along $〈001〉$ and $〈111〉)$, yet gives results virtually indistinguishable from ordinary $\mathbf{k}\cdot \mathbf{p}$ theory. A unique operator ordering is established for heterostructures, and example calculations on superlattices show good results.

• Received 7 July 1997

DOI:https://doi.org/10.1103/PhysRevB.56.R12748