Research On The Interface Phenomena Of Topological Materials

The study of topological materials such as topological insulators and topological superconductors is one of the hottest topics in contemporary condensed matter physic-s. Topological insulators have a insulating gap in the bulk and gapless edge or surface states. Topological superconductors which support Majorana fermions at surface or at vortices are characterized by a pairing gap in the bulk and gapless surface states. Because of these intriguing and exotic properties, there will be many interesting phe-nomena at the interface between topological materials and others, which are what we concern. This dissertation consists of four chapters.In chapter one, we introduce the basic concepts and theory of topological material-s. First, we present the concept of Berry phase. Then, quantum Hall effect, topological insulators, topological superconductors, and topological semimetal are introduced and explained from a topological point of view. Last, the content and significance of our research are given.In chapter two, we firstly investigate the Fresnel coefficients for the reflected and refracted electromagnetic waves across the interface between three-dimensional topo-logical insulators and left-handed metamaterials. Then, we derive the exact analytic expressions for Kerr and Faraday rotations. By way of multiple reflections method, we demonstrate that perfect lens with left-handed metamaterials slab and topological in-sulators can be designed. On the other hand, the processes of reflection and refraction are investigated in the case of topological insulator and chiral metamaterial. Then, we give the reflection and transmission coefficients of topological insulator with a chiral medium slab. Lastly, the potential applications of these results are discussed. In chapter three, the tunnel junction of an s-wave superconductor (SC) coupled to two spatially separated fractional quantum Hall (FQH) liquids is investigated theoret-ically. The reflection of quasiparticles and Cooper-pairs on the junction has different properties in different coupling limit. In the weak coupling limit, the reflection process is perfect reflection process. However, in strong coupling limit, there is the phenom-ena of crossed Andreev reflections in which a set of quasiparticles are reflected as quasiholes on every FQH liquid side and transmit as Cooper-pairs to the SC side. The numbers of quasiparticles and quasiholes involved in the AR process satisfy a specif-ic selection rule. In addition, such setup can also creat spin singlets of two electrons which are spatially separated and act as an entangler.In chapter four, we make a conclusion of this dissertation, and then present some outlook for the investigation.