Luttinger-like parameter calculations - art. no. 235302

We have calculated the Luttinger-like parameters, used in the 8 x 8 Hamilto nian describing both conduction and valence bands, via a second-order pertu rbation theory that allows one to make the Lowdin renormalization valid for a set of nondegenerate energy levels. We show that the formulas given in t he paper by Pidgeon and Brown [Phys. Rev. 146, 575 (1966)] are the correct ones, contrary to what is claimed in recent papers. This leads to strong di screpancies when the spin-orbit splitting is not much smaller than the band gap. For example, the ratio between the Luttinger-like parameters <(<gamma >)over tilde>(1), calculated in the two cases, is of the order of 1.5 in Ga As, 3 in InAs, and 16 in InSb. The accuracy of the equations used by Pidgeo n and Brown is also discussed.