Pseudoultrarelativistic behavior and specification of spinlike effects in the two-dimensional electron gas in Kane semiconductors with direct and inverted band structure

The comparative study of the spin splitting of two-dimensional subbands in surface layers on small gap Hgₓ{Cd}_{1{{-}}x}$Te, with direct (${E}g0) and inverted ({E}g$0) bands, is carried out experimentally and theoretically. The occupations of spin-splitted subbands ${n}ᵢ⁺$ are determined from Fourier transforms of capacitance magneto-oscillations of ${Hg}ₓCd_1-xTe metal-oxide-semiconductor structures. The values (nᵢ^--nᵢ⁺)/(nᵢ^-+nᵢ⁺) are found to be independent of surface densities nₛ, subband index i, and |Eg| at high enough nₛ when the band bending sufficiently exceeds the gap Eg and the conditions corresponding to pseudoultrarelativistic behavior of surface electrons are fulfilled. However, they are different for Eg{}0 and Eg0 cases. To analyze spinlike effects in narrow-gap and gapless semiconductors, we employed for Kane Hamiltonian the conception, offered by Zel'dovich and Migdal for the description of vacuum condensate of Dirac's electrons near supercritical nuclei. In this way, we obtain ``usual'' Schrodinger-like subband equations with some effective potential. The terms responsible for nonparabolicity, spin-orbit splitting, and ``resonant'' shift, due to interband mixing by surface electric fields, are easily singled out. Such equations admit the simple physical interpretation, and difference in values of ``spin'' effects for Eg{}0 and Eg0 cases is easily seen. The dependencies of total subband occupations nᵢ=nᵢ^-+nᵢ⁺ and average cyclotron masses on nₛ nevertheless are close for both cases in agreement with previous experimental observations. In a pseudoultrarelativistic limit Eg=0 the simple analytical expressions for subband parameters of experimental interest are obtained with an allowance for spin effects. The calculations agree with experiment for Hgₓ{Cd}_{1{{-}}x}$Te with both direct and inverted bands, excluding the region of low ${n}ₛ$ in heavily doped samples. Possible reasons for disagreement are discussed. {} 1996 The American Physical Society.