题 目：Topological Insulators: Dimensionality, Magnetic Field and Disorder
The talk has three sections. In the first section, a brief review about topological insulator will be introduced. Then I will investigate the problem of three dimensional topological insulator (3DTI) in a magnetic field. The quantum Hall states of this system are exhibited by side surface states, rather than edge states in 2D. A new definition and experimental setup of quantum Hall effect are proposed. The last section focuses on the origin of topological Anderson insulator (TAI) in 2D. The TAI phase is triggered by a band touching as a second perturbation effect from disorder, and lives in a cluster of nontrivial subgaps surviving through size scaling and statistical average.