Studies On Spin-polarized Transport Properties In A Fractal Semiconductor Multilayers Heterostructures

In this paper we investigate theoretically the spin-polarized transport properties of electrons tunneling through fractal semiconductor multilayers with two ferromagnetic contacts (F/FSM/F) in the presence of a spin-orbit interaction, which possess great potential in future applications. The spin-polarized transport properties of the F/FSM/F heterostructures are compared with that of periodic semiconductor multilayers again with ferromagnetic contacts (F/PSM/F). We expect to provide theoretical foundation for the development of nonlinear spintronic devices with our work. The main results obtained in this paper are listed below:(1) F/FSM/F heterostructures, a type of F/S/F having a self-similar structure have been introduced. A given F/FSM/F heterostructure can be understood as a strictly periodic F/PSM/F heterostructure with defects.(2) On the basis of coherent quantum theory, we have systematically investigated spin-polarized electron transport through the F/FSM/F and corresponding F/PSM/F heterostructures with and without randomly distributed variations in the semiconductor layer thicknesses but in the presence of a spin-orbit interaction. The dependence of the transmission coefficients for the two different structures on the degree of complexity, n , the total thickness of the SM structure, the strength of the Rashba spin-obit coupling and the degree of randomness in the semiconductor layer thicknesses has been discussed. The numerical results show that transmission spectra of the F/FSM/F heterostructures posses some distinctive properties, such as stability against the effects of randomness in the layer thicknesses, sharp localized resonances, and a more marked quantum size effect than in non-fractal structures. We have found that the transmission for spin-up and spin-down electrons can be separated not only in the P magnetizations but also in the AP magnetizations, which is different from the case for these structures without fluctuating layer thicknesses.(3) Fractal behavior in spin electron transport has been studied by means of the correlation coefficient. The correlation coefficient shows how the transmission coefficient for the F/FSM/F heterostructures has a self-similar structure associated with the fractal distribution of the SM structure. In other words, transmission spectra of the F/FSM/F heterostructures posses scalability than in non-fractal structures. This property illustrates a clear and direct correlation between the geometry of a structure and the spectra of resonant transmission.(4) On the basis of coherent quantum theory and the Landauer-Büttiker scattering formalism, we have systematically investigated the spin-dependent shot noise properties of electron tunneling through the fourth-stage F/FSM/F and the corresponding F/PSM/F heterostructures in the presence of the Rashba spin-orbit interaction and an electric field. The dependences of the current, shot noise and Fano factor for the two different structures on the total length of the SMs structure, the Rashba spin-obit interaction, the external bias voltage, and the angle between the magnetic moments in the two ferromagnetic contacts have been numerically calculated and discussed. The results indicate that the shot noise becomes strongly spin-dependent and can be greatly modulated not only by the external electric field and Rashba spin-orbit interaction, but also by the structural configuration and length of the semiconductor multilayers.(5) Compared to the F/PSM/F heterostructures, the current, shot noise, and Fano factor of the F/FSM/F heterostructures can exhibit a more marked quantum size effect, along with typical low-frequency aperiodic oscillations as the bias voltage or the Rashba spin-orbit coupling strength increases. There is little Rashba spin-orbit coupling strength dependence with increasing angle between the two magnetic moments of the left and right ferromagnets. Our results have further demonstrated that the F/FSM/F heterostructures have possible superiority over F/PSM/F heterostructures for the implementation of quasi-one-dimensional spin-transistor devices and the design of quantum coherent spintronic devices. Our results may thus shed light on and encourage further study of the subtle mechanisms in mesoscopic transport processes and help optimize the design of future spintronic devices.