A NEW APPROXIMATION FOR BLOCK DIAGONALIZING THE 8-BAND K-CENTER-DOT-P-HAMILTONIAN

Kane's (1957) coordinate transformation for diagonalizing the eight-ba nd k.p Hamilton matrix for GaAs-like semiconductors into 4x4 blocks is reexamined, where the k(2)-terms (free electron and interaction with the remote bands) are taken into account fully, not only perturbativel y. Then, the warping precludes an exact block diagonalization. A new a pproximation is proposed which allows for a 4x4 block diagonalization, again. Since this approximation preserves the cubic symmetry and its error vanishes along the symmetry directions (k parallel to [100], [11 0], [111], etc.), it remains small for general k-directions. This is i llustrated by numerical examples. The 4x4 block diagonalization allows for significant simplifications in calculating the band structure and related properties. In contrast to other approaches, a consistent cal culation of the momentum matrix remains possible.