Anomalies in the magnetoreflection spectrum of bismuth in the low-quantum-number limit

Abstract

We report here anomalies observed at high magnetic fields in the magnetoreflection line shape of bismuth $\overrightarrow{H}$ parallel to binary, bisectrix axes) and bismuth-antimony alloys $\overrightarrow{H}$ parallel to binary axis) and associated with Landau-level transitions originating from the lowest-quantum-number $j=0\mathrm{}$ levels of the valence and conduction bands. Also reported are the corresponding Shubnikov-de Haas measurements made in steady magnetic fields up to 220 kG. To interpret these anomalous magnetoreflection line shapes an accurate model for the dispersion relations of the two coupled $j=0\mathrm{}$ magnetic energy levels is developed, including the dependence of the magnetic energy levels on the magnetic field and on the wave-vector component parallel to $\overrightarrow{H}$. This model is applied to the interpretation of the Shubnikov-de Haas data and to a magnetoreflection line-shape calculation for the experimental conditions under which these anomalies are observed. The calculated line shapes successfully reproduce the large variety of observed line-shape anomalies as well as their relative intensities, thereby providing strong support for this description of the dispersion relations for the $j=0\mathrm{}$ magnetic energy levels.