Spin-polarized electron states in a quantum film based on narrow - band semiconductors

Narrow--gap semiconductors (NGS) with strong spin-orbit interactions are promising materials as a source of polarized electrons. Electron states in NGS are described by the Dirac-type equation with Hamiltonian parameters determined by the Kane interband matrix element [1]. Modern epitaxial technology makes it possible to create quantum films (QF) (or quantum wells) with a \textit{given }spatial dependence of the composition, $i.e$. control of the position-dependence of the energy gap. The electron dispersion in a homogeneous QF with same boundaries still keeps the spin degeneracy [2]. In the present work it is shown that the position dependent gap leads to spin-splitting of the electron dispersion in a QF. For a film with a \textit{linear} spatial gap variation in the transverse direction, the solution of the Dirac equation can be found exactly. Near the gap the proposed spin-orbit mechanism approximately reduces to Rashba's term with the loop in dispersion. The electron polarization degree for a QF based on a \textit{Pb}$_{1-x}$\textit{ Sn}$_{x}$\textit{ Te} system is calculated. [1] J. O. Dimmock \textit{et al}, Phys. Rev. \textbf{16}, 1193 (1966). [2] S.Yu. Potapenko and A. M. Satanin, Sov. Phys. Solid State \textbf{26}, 1067 (1984).