Spin channels exploring finite superlattices: Vertical and lateral transport

Abstract

We have investigated spin-dependent transport properties in finite semiconductor superlattices containing $N$ periods. Spin-orbit coupling is taken into account by including the linear Dresselhaus term into the effective Hamiltonian. We have derived analytical expressions for spin-polarized transmission coefficients, density of states, group velocities, and phase delay times for these systems. It is shown that the miniband structure of infinite semiconductor superlattices is spin dependent and plays a fundamental role in the description and understanding of these quantities. For $N$-period superlattices, these quantities are oscillating functions of the electron energy and their maxima and/or minima are always localized inside the corresponding spin-split minibands. The oscillations disappear for energies inside the superlattice minigaps. We have identified two electron energy ranges where the spin-split minibands do not show overlap and, within these energy ranges, the polarization efficiency is essentially 100%, suggesting that these systems may be explored as possible spin filtering mechanism, even for unpolarized injection from the emitter layer. It is also shown that the energy range where the spin-split resonant minibands show overlap may be also explored as lateral multichannel spin filters, but their efficiencies depend on the degree of resonant peak overlapping.