P. Enders, A NEW APPROXIMATION FOR BLOCK DIAGONALIZING THE 8-BAND K-CENTER-DOT-P-HAMILTONIAN, Physica status solidi. b, Basic research, 187(2), 1995, pp. 541-550
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.