Andreev Reflection In A Metal-topological Superconductor Hetero-junction System

In recent years, topological insulators have become one of the most attractive areas in condensed matter physics, and another direct and important analogy of the topological insulators which is known as topological superconductors have also been proposed. Topological superconductors are distinct from normal superconductors by their novel robust gapless edge states. The main difference between topological superconductors and topological insulators is that the former do not need time reversal symmetry as the latter do, but on the other hand it must satisfy particle-hole symmetry. We can divide topological superconductors into different categories by several kinds of symmetries that the Hamiltonian satisfies and the dimensions of the materials.This paper is organized as follows. The first chapter is an introduction to superconductor, the Bd G mean field theory and the BTK theory of Andreev scattering, then we introduce some basic concept and the background of the topological superconductors,although its existence has not been confirmed experimentally.In the second part we investigated one of the simplest models of topological superconductors, the Read-Green model. By choosing appropriate parameters, we find the existence of the chiral gapless edge state. This edge state does not conserve time reversal symmetry. Later, we exploit this model to construct the Hamiltonian of normal metal/topological superconductor hetero-junction system, and then we use the non-equilibrium Green’s function method to investigate the Andreev reflection probabilityThe third chapter discusses physical quantities that affect the Andreev reflection probability. Then we make some discussions about the results and point out some deficiency in this research.