Quantum Spin Hall Effect And Topological Insulator

Fractional quantum Hall Effect (FQSH) is one of most fundamental issues in condensed matter physics, and the Topological insulator becomes its prominent applications. This article reviews the general frameworks of these development and the physical properties. FQSH states and topological insulators are supposed to be topologically invariant under the minor change of geometrical shape or internal impurities. The phase transitions involved in this phenomena are known not to be explained in terms of symmetry breaking or Landau-Ginsburg theory. The new type of phase transitions related to topological invariants has acquired new name - topological phase transition. The intuitive concepts and the other area having same type of phase transitions are discussed.