Parameter consistency in multienergetick⋅pmodels

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Abstract
Standard derivations of multiband k⋅p models rely on Löwdin perturbation theory. Close examination of this method, however, reveals that it is unsuitable for treating systems with multiple zeroth-order energies. As a result, various perturbation sums in multienergetic k⋅p models are not well defined, and a consistent set of k⋅p parameters cannot be guaranteed. We inspect this difficulty and present an alternative derivation of the k⋅p theory based on the method of infinitesimal basis transformations. This approach clearly demonstrates that a consistent k⋅p matrix can be generated from an arbitrary number of zeroth-order wave functions regardless of their energies. In addition, we obtain a corrected expression for off-diagonal perturbation sums. The expression is applied to give the corrected form for the asymmetric B parameter in the s-p-coupled zinc-blende k⋅p Hamiltonian.