Nonequilibrium electronic transports through a system hosting three quantum dots hybridized with superconductors are investigated. By tuning the relative positions of the dot levels, we illustrate the existence of Majorana fermions and show that the Majorana feimions will either survive separately on single dots or distribute themselves among different dots with tunable probabilities. As a result, different physical mechanisms appear, including local Andreev reflection（LAR）,cross Andreev reflection（CAR）, and cross resonant tunneling（CRT）. The resulting characteristics may be used to reveal the unique properties of Majorana fermions. In addition, we discuss the spin-polarized transports and find a pure spin current and a spin filter effect due to the joint effect of CRT and CAR, which is important for designing spintronic devices.
Transport properties are theoretically studied through an anisotropy single-molecule magnet symmetrically connected to two identical ferromagnetic leads. It is found that even though in parallel configuration of leads’ magnetizations, the total current still greatly depends on the spin polarization of leads at certain particular bias region, and thus for large polarization a prominent negative differential conductance （NDC） emerges. This originates from the joint effect of single-direction transitions and spin polarization, which removes the symmetry between spin-up and spin-down transitions. The present mechanism of NDC is remarkably different from the previously reported mechanisms. To clarify the physics of the NDC, we further monitored the shot noise spectroscopy and found that the appearance of the NDC is accompanied by the rapid decrease of Fano factor.
