Fourier Expansion for Electronic Bands in Trigonal Tellurium and Selenium

Abstract

The Fourier expansion technique for coupled bands is applied to the electronic dispersion relations of solids which crystallize into structures with ${D}_{3}^{4}$ (or ${D}_{3}^{6}$) symmetries. In this treatment, the spin-orbit interaction is included. A magnetic Hamiltonian is developed which is valid throughout the Brillouin zone. When $H$ is parallel to the $c$ axis, the Landau-level energy eigenvalues can be obtained as a one-dimensional Fourier expansion in ${k}_{z}$. Selection rules for optical transitions in a magnetic field are presented.