Decoupling of Majorana bound states in T-shaped double-quantum-dot structure with ferromagnetic leads

Abstract

The potential huge application value of the Majorana bound states (MBS) in topological quantum computing highlights the importance and necessity of the relevant in-depth research. To understand the physical properties of MBS, the most feasible way is to connect it to a mesoscopic circuit to investigate the quantum transport behaviors. Based on this idea, we study the transport properties in the systems with MBS, and provide theoretical support for its further understanding and detection, with the help of the nonequilibrium Green's function method and scattering matrix theory. To be concrete, we perform theoretical investigation of the transport properties in the T-shaped double-quantum dot structure, by considering MBS to be coupled to the dot in the main channel. It is shown that in the linear transmission region, as the level of side-coupled dot is tuned to the Fermi energy level, the contribution of MBS to the conductance is erased in the case of weak and strong Coulomb interaction. When the side-coupled dot departs from the Fermi energy level, they present different results. When Majorana zero mode is added, the linear conductance is independent of the level of the side-coupled quantum dot, and the conductance plateau appears. However, with coupling between the MBSs, the linear conductance is the same as the case without the MBSs. The decoupling phenomenon of the MBSs remains robust. Therefore, the signature of the MBSs can be erased by tuning the level of the side-coupled quantum dot or the inter-MBS coupling. When ferromagnetic leads are introduced, the appearance or disappearance of the conductance plateau are clearly dependent on the difference between the magnetic field and the lead polarization directions in the system, whereas the decoupling behavior of the MBSs survives. This work contributes to further explanation of the decoupling phenomenon of MBSs in the T-shaped double-quantum-dot system, and provides theoretical approach for deeper understanding and detection of the MBS.