Abstract
We investigate theoretically the transmission properties of electrons tunneling through fractal semiconductor multilayers (FSMs) sandwiched between two ferromagnets (Fs) in the presence of a spin-orbit interaction. Calculations are carried out with and without presumed randomly distributed uncertainties in the semiconductor layer thicknesses. Within the Landauer framework of ballistic transport and using transfer matrix methods, the transmission coefficients of the F/FSM/F heterostructures are numerically calculated and compared with that of periodic semiconductor multilayers (PSMs) again with ferromagnetic contacts. The results indicate that the transmission spectrum of the F/FSM/F heterostructures has partially self-similar properties as well as stability against the effects of random variations in layer thicknesses. Furthermore, compared to the F/PSM/F heterostructures, the transmission spectrum of the F/FSM/F heterostructures exhibits sharp localized transmission peaks and a more marked quantum size effect. Interestingly, for the case with random layer-thickness fluctuations, the transmissions for spin-up and spin-down electrons can be separated when the magnetizations of the left and right ferromagnetic layers are antiparallel. This is quite different from the case without random layer-thickness fluctuations.
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