Theoretical Study Of Majorana Fermions And Spin Transport Properties In Double Quantum Dots System

In the21st century, the use of nanotechnology greatly changed people’s lives, and promote the development of society. Its rapid development stimulates scientists to research extensively on mesoscopic systems. The quantum effect in nanostructure, such as quantum confinement effect to make a qualitative change in many physical properties, showing many different from the macroscopic objects and is also different from the phenomenon of a single atom. So the research of mesoscopic system has significant and far-reaching impact on nanotechnology application. In this paper, we mainly use the non-equilibrium Green’s function method to study the typical meso-scopic structures-quantum dots transport properties, and use the transport properties of quantum dots to detect Majorana fermions.In the first chapter, we introduce the basic concepts and basic theory of meso-scopic transport, discussed the issue of quantum transport regime and quantum trans-port channels in the mesoscopic systems. Simultaneously, we introduce the Landuaer-Buttiker formula which is wildly used in the transport of mesoscopic systems. And then, the Aharonov-Bohm effect in mesoscopic systems due to quantum interference. We give a brief introduction of characteristics of the quantum dots, Fano resonance and Coulomb blockade effect in quantum dots system. Meanwhile, a brief introduc-tion of the more popular condensed matter theory about topological superconductors, topological insulators and basic concepts of Majorana fermions. Spintronics is a more promising research on the application of nanotechnology. The spin coloritronics which combines thermoelectric and spintronics, refers the conversion of energy-voltage in spintronics application. In the second chapter, we propose a scheme for detecting Majorana fermions in the topological material. The Aharonov-Bohm interferometer can be formed by going through a flux in the loop of parallel double quantum dots system. Two quantum dots connecting to two ends of a one-dimension topological superconductor, we investigate the linear conductance of system by means of quantum coherent effect of transport electrons in the Aharonov-Bohm interferometer. Two special cases are discussed, the topological superconductor nanowire being grounded directly and grounded indirect-ly by a capacitor with strong Coulomb energy. In the former case, we find fixed a zero-bias unit conductance peak independent of other parameters on the condition of coupling between quantum dots and Majorana bound states. In the other case, the An-dreev reflection effect occurring on the quantum dot and topological is blocked duo to the strong Coulomb effect. This bring up a conception-teleprotation, which indicates electrons transport from one end to the other across two spatial separated Majorana bound states keeping coherence. This behavior is similar with transport in a single level quantum dot, but a addition phase in teleportation make it different with quan-tum dot. A new resonant conductance peak emerges among two fundamental resonant conductance peaks, the oscillation of conductance reveals4πn and by changing a charge number in capacitor show a2?r phase shift. These phenomena suggest the existence of Majorana fermions.In the chapter3, we apply a temperature gradient and a same magnetic field on double quantum dots which sandwiched between two nonmagnetic electrodes. By tun-neling two gate voltages of quantum dots separately. we can create a electron transport on one quantum dot with a definite spin while a hole transport on the other one with the opposite spin. In electronic view, two contrary spin electrons which transport through t-wo quantum dots independently in the opposite direction. If the current of two quantum dot are same amplitude but with opposite spin and direction, then, the pure spin current accompany vanishing of the charge current. We discuss the different spin current at different quantum dots energy levels, reveals that the generation and manipulation by electric means, need not the ferromagnetic leads, switching of magnetic field or spin-orbital interaction. The thermopower and figure of merit of spin are also discussed. We find that the charge Seebeck coefficients equals zero but spin Seebeck coefficient is not at the points of pure spin current emerge. At the particle-hole symmetry points, the pure spin current occurring being independent of magnetic and temperature different.Finally, we make a conclusion of this thesis, and a prospect investigations is pre- sented in the last chapter.