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

Abstract

Direct interband magneto-optical transitions have been observed at k=0 in InSb using the reflection technique at 1.5\ifmmode^\circ\else\textdegree\fi{}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 (${\ensuremath{\gamma}}_{3}\ensuremath{-}{\ensuremath{\gamma}}_{2}$) 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: $({\ensuremath{\gamma}}_{3}\ensuremath{-}{\ensuremath{\gamma}}_{2})=1.2\ifmmode\pm\else\textpm\fi{}15%$, $q=0.4\ifmmode\pm\else\textpm\fi{}50%$, and $C=6.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ a.u. \ifmmode\pm\else\textpm\fi{}30%. This value of $C$ is about 4.5 times smaller than an erroneous value published previously.