Transport Properties In Topological Insulator-superconductor Nanostep Junctions And Majorana Fermions Coupled With Quantum Dots

In this thesis, we investigated the transport property in topological insulators. We calculate and research for two sections: Suppression of Andreev conductance in a topological insulator(TI)-superconductor nanostep junction and transport properties of thermal electrons in Majorana bound states coupled with two quantum dots.In the first place, we calculate the conductance in a topological insulator-superconductor nanostep junction through transfer matrix method. When two three-dimensional(3D) topological insulators(TIs) are brought close to each other with their surfaces aligned, the surfaces form a line junction. Similarly, three TI surfaces, not lying in a single plane, can form an atomic-scale nanostep junction. In this thesis, Andreev reflection in a TI-TI-superconductor nanostep junction is investigated theoretically. Because of the existence of edge states along each line junction, the conductance for a nanostep junction is suppressed. When the incident energy( ?) of an electron is larger than the superconductor gap( ?), the Andreev conductance in a step is less than unity while for a plane junction it is unity. The Andreev conductance is found to depend on the height of the step junction. The Andreev conductance exhibits oscillatory behavior as a function of the junction height with the amplitude of the oscillations remaining unchanged when ? ?0, but decreasing for ? ? ?, which is different from the case of the plane junction. The height of the step is therefore an important parameter for Andreev reflection in nanostep junctions, and plays a role similar to that of the delta potential barrier in normal metal-superconductor plane junctions.And then we research the transport properties of thermal electrons in Majorana bound states coupled with two quantum dots for two types of models with Majorana fermions: T type structure and series connection structure. In addition, for the sake of comparison, we researched the thermal transport properties of T type structure and series connection structure without Majorana fermions. In general, when the energy levels of quantum dots are below ?, the main carriers are holes which are excited in the system and then the thermal power S is positive. When the energy levels are above ?, the main carriers are electrons which are excited in the system and thus the thermal power S is negative. However, more particularly, in the structure we have researched, the thermal power S in the T type structure with Majorana fermions does not behave generally. Instead, the sign of thermal power S changes from negative to positive when the energy levels of quantum dots are below ? while the sign of thermal power S changes from positive to negative when the energy levels of quantum dots are above ?. In addition, the dimensionless figure of merit ZT is decreased first and then increased with the increase of temperature. What’s more, compared with the structure without Majorana fermions, the structure with Majorana fermions, no matter T type or series connection structure, the dimensionless figure of merit ZT is suppressed.