Excitonic Effects in Landau Transitions at theE1Edges of InSb and GaSb

Measurements are presented of differential reflectivity in a strong magnetic field in InSb and GaSb at the $E_1$ and $E_1+{\Delta }_1$ edges. A description of the circular-polarization modulation technique used to obtain the data is given. Optical absorption at a critical point along the [111] direction in a semiconductor lacking inversion symmetry is discussed. An exciton model in a magnetic field is developed. Numerical solutions for the first four bound-state energies having azimuthal quantum number $m=0\mathrm{}$ are tabulated for the two-dimensional Schrödinger equation of an attractive Coulomb potential in a magnetic field. Solutions to the three-dimensional problem are discussed using the Born-Oppenheimer approximation. The exciton model is compared to experimental spectra of Landau levels at the $E_1$ edge of InSb. A value of 2.8 ± 0.6 meV is obtained for the exciton rydberg. This agrees with the value obtained using the measured effective transverse mass $\frac{m}{{\mu }_t}=19.7\mathrm{}\pm 1.3$ and the static dielectric constant of InSb. A lower limit on the longitudinal mass of $15\lesssim \left|\frac{{\mu }_l}{{\mu }_t}\right|$ is estimated. The sign of the longitudinal mass has not been unambiguously obtained; however, the critical-point symmetry at the $E_1$ edge may be of type $M_0$ instead of $M_1$. The $E_1$ excitonic energy gap is determined to be 2.015 ± 0.001 eV. Spectra of GaSb are compared to InSb. A line splitting of 33 meV due to the inversion asymmetry in GaSb is proposed.