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Recent work by Elder, Ward and Zhang [Phys. Rev. B83. 165210 (2011)] hasshown need for correction and modification of current implementation of the k.pmethod and operator ordering scheme using the interaction parameters definedunder double group consideration. This manuscript examines the difference intreatment of spin-orbit interaction under the single and double groupformulations. We show that the restriction to the adapted double group bases,brought about by the imposition of single group selection rule in calculatingthe k.p interaction, is not appropriate. In addition, the unitarytransformation employed in the literature to diagonalise the intra-band spinorbit interaction in semiconductors with diamond lattice can not remove theinter-band terms. It leads to a bases set for valence band ordered differentlyfrom D_3/2^+ in the O(3) group thus invalidating any correlation of magneticquantum number to the z component of angular momentum. Under the double groupconsideration, spin-orbit interaction affects all the zone centre states andoffers a mechanism for changing the relative positions of various zone centrestates in the conduction band. In addition to the mixing caused by kindependent spin orbit terms, formation of hybridised orbitals under doublegroup rules also produce mixing. This can lead to inversion in materials suchas \alpha-tin. The re-arrangement of conduction band zone centre states leadsto a negative \gamma_2 in most materials with respect to the valence band baseshaving the same order as D_3/2^+ in the O(3) group. The double groupformulation is also required in the description of Zeeman interaction,including the S.B term, for the mixed zone centre states. It provides acorrespondence between second order interaction parameters and the Luttingerinvariants. ...

Spin-orbit interaction in the k \cdot p theory for cubic crystals