Inversion-Asymmetry and Warping-Induced Interband Magneto-Optical Transitions in InSb

Direct interband magneto-optical transitions have been observed at k=0 in InSb using the reflection technique at 1.5°K. In addition to the normal spectral structure associated with allowed transitions, some strong features have been observed associated with "extra" transitions produced both by the warping and the linear-in-k splitting of the valence band of InSb. An unambiguous assignment of the origin of these transitions has been made by a study of the anisotropy of the spectra [with the magnetic field H in the (110) crystal plane] using left and right circularly polarized light. With the allowed and extra transitions, we can determine the relative energies of the first five valence-band magnetic energy levels. By fitting these, and the strengths of the extra transitions, we determine Luttinger's warping parameter (${\gamma }_3-{\gamma }_2$) and the Dresselhaus inversion-asymmetry parameter C. In addition, it is necessary to retain Luttinger's parameter $q$, which normally has been assumed to be zero. This quantity is present in the effective-mass Hamiltonian when there is a magnetic field and spin-orbit interaction. We find: $({\gamma }_3-{\gamma }_2)=1.2\mathrm{}\pm 15\%$, $q=0.4\mathrm{}\pm 50\%$, and $C=6.6\mathrm{}\times {10}^{-4\mathrm{}}$ a.u. ±30%. This value of $C$ is about 4.5 times smaller than an erroneous value published previously.