Invariant expansion of the 30-band k·p model and its parameters for III-V compounds

In this paper, we derive a ready-to-use symmetry-invariant expansion of the full-zone 30-band $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ Hamiltonian for the ${T}_d$ point group. To find respective parameters, the band structures of III-V materials were calculated within a state-of-the-art density functional theory (DFT) approach and used next as targets to adjust the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ bands. A satisfactory agreement of the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model with the DFT band structures, for all tested zinc-blende III-V semiconductors, has been achieved. Values of many of the parameters have not been known so far. We also compare the fitted $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ parameters with the values calculated using momentum matrix elements obtained directly from DFT.