Variational formulation of stable discrete k·p models

The longstanding problem of spurious states in k·p models of semiconductor nanostructures has been shown to be an artifact of the use of the centereddifference approximation to the gradient, and it has been shown that stable models may be constructed on the basis of lower-order one-sided differences. The present paper demonstrates how the resulting bulk bandstructure models may be applied to heterostructures without introducing anomalies in the wavefunction behavior. This is done by constructing a variational functional in which the desired wavefunction continuity and boundary values are explicitly inserted, and then deriving the discrete Hamiltonian from that functional.