Transport Properties Of System With Majorana Bound States

In recent years, Majorana bound states, obeying an exotic form of quantum statistics called non-Abelian statistics, can be used as the simplest platform for realizing topological quantum information processing. These properties have attracted increasing attention. In this paper, we focus on the properties of the Majorana bound states and the methods to probe the existence of the Majorana bound states.Firstly, to understand the effect of photon assisted tunneling(PAT), the effect of an ac electric field on quantum transport properties in a system of three quantum dots, two of which are connected in parallel, while the third is coupled to one of the other two, is investigated theoretically. Based on the Keldysh nonequilibrium Green’s function method, the spin-dependent current, occupation number, and spin accumulation can be obtained in our model. An external magnetic flux, Rashba spin-orbit-coupling(SOC), and intradot Coulomb interactions are considered. The magnitude of the spin-dependent average current and the positions of the PAT peaks can be accurately controlled and manipulated by simply varying the strength of the coupling and the frequency of the ac field. A particularly interesting result is the observation of a new kind of PAT peak and a multiple-PAT effect that can be generated and controlled by the coupling between the quantum dots. In addition, the spin occupation number and spin accumulation can be well controlled by the Rashba SOC and the magnetic flux.Secondly, Employing the Keldysh Nonequilibrium Green’s function method, we investigate time-dependent transport through a topological superconductor with Majorana bound states in the presence of a high frequency microwave field. It is found that Majorana bound states driven by photon-assisted tunneling can absorb(emit) photons and the resulting photon-assisted tunneling side band peaks can split the Majorana bound state that then appears at non-zero bias. This splitting breaks from the current opinion that Majorana bound states appear only at zero bias and thus provides a new experimental method for detecting Majorana bound states in the non-zero-energy mode. We not only demonstrate that the photon-assisted tunneling side band peaks are due to non-zero-energy Majorana bound states, but also that the height of the photon-assisted tunneling side band peaks is related to the intensity of the microwave field. It is further shown that the time-varying conductance induced by the Majorana bound states shows negative values for a certain period of time, which corresponds to a manifestation of the phase coherent time-varying behavior in mesoscopic systems.Lastly, employing the recursive Green’s function method, we investigate the Josephson current through a quantum dot side coupled to a topological superconducting nanowire sustaining a pair of Majorana bound states. It is found that the Josephson current is blocked when the quantum dot is side coupled to a superconducting nanowire in a topologically trivial phase. However, when the topological superconducting nanowire transitions from a topologically trivial to a topologically non-trivial phase, an Andreev bound state arises at the zero Fermi energy of the quantum dot due to leakage of the Majorana bound states. Thus a Josephson current can be induced by leakage of the Majorana bound states into the quantum dot. The Josephson current shows a plateau-like structure and a clear-cut trivial/non-trivial phase transition, as a function of a Zeeman field imposed on the system. The transition and plateau-like structure can be used to probe the existence of the Majorana bound states. The current-phase relation has also been studied.