The energy spectra of narrow-gap semiconductor heterostructures: spin splitting in the case of asymmetry

Using the two-band model, the energy spectrum is explicitly obtained as a function of the spin projection and transverse momentum for two abrupt semiconductor heterostructures of type II: (i) a double heterojunction and (ii) a system of two quantum wells, one in the valence band and one in the conduction band. The transverse motion of the carriers and the effective repulsion of the electron-like and hole-like energy levels give rise to effects which cannot be properly described in the framework of the single-band theory. The two special cases form the basis for a discussion of the properties of more general classes of heterostructures of any type. The spin splitting of the energy spectrum is found to be a characteristic property of asymmetric heterostructures. Degeneracy occurs in the case of spatially symmetric heterostructures and for a class of heterostructures which are spatially asymmetric but symmetric with respect to energy. The possibility of a new type of transition is discussed.