拓扑绝缘体、拓扑（超流）超导体的基本性质及其应用的研究是最近几年理论物理和实验物理中刚涌现出一新的、令人十分兴奋的、有重要学术价值和应用前景的研究领域。这些拓扑相的表面态(边缘态)导致一个与任何已知一维或二维电子体系具有不同特性的导态。这些特性在自旋电子学和拓扑量子计算方面将有重要的应用前景。本项目计划通过对拓扑绝缘体、拓扑（超流）超导体的表面态（边缘态）基本特性和电子、自旋输运特性，和外场、磁性杂质和各种其他材料的异质结构对其表面态（边缘态）基本特性和电子、自旋输运特性的影响，以及拓扑相的基本特性的应用方面进行系统深入的研究，为该研究领域的发展做出具有原创性的重要贡献。同时对拓扑相和冷原子体系中的Majorana费米子态和寻找Majorana费米子的理论方案，及其在拓扑量子计算中的应用进行深入研究。

That the study on properties of topological insulators and topological (superfluid) superconductors and their applications have become a novel, exciting, important and significant research field in theoretical physics and experimental physics. The surface (or edge) states of a topological insulator and topological (superfluid) superconductor lead to a conducting state with properties that are unlike any other known 1D or 2D electronic systems. These special properties can be useful for applications ranging from spintronics to quantum computation. In this project, we plan to study the fundamental properties of the surface (or edge) states of the topological insulators and topological (superfluid) superconductors, properties of transport of electrons and spins in these surface states, the responses of the fundamental properties of the surface (or edge) states and transport of the electrons and spins to the external magnetic fields, to magnetic impurities, to magnetic coats, etc, and the applications of these new properties. We hope obtain some important and significant creative achievements from these research project. Meanwhile, we study on the properties of Majorana Fermion in these topological states and ultracold atom systems, find realizable and improved theoretical scheme for how to search and probe for Majorana Fermions in these topological states and in ultracold atom systems, and study their applications to topological quantum computation.