报告题目：Topological Quantum Materials and Others
报告摘要：Topology is an old branch of mathematics, and is now becoming an efficient to discover new phases of matter. In the last decade, prediction and discovery of topological insulators and other materials is the most significant progress in condensed matter physics and material sciences on topological matericals. Topological insulator is an insulator that always has a metallic boundary. These metallic boundaries originate from the topology of the band structure of solids, which is insensitive to the geometry of system and cannot change as long as the material remains insulating. The first topological state of matter is the quantum Hall state, the Hall conductance of which is insensitive to continuous changes in the parameters and depends only on the number of edge states, which are unidirectional because of the breaking of the time reversal symmetry due to the magnetic field. This effect was generalized to the system with time reversal symmetry, such as graphene with spin orbit coupling and an "inverted" semiconductor HgTe/CdTe quantum well, exhibiting the phenomenon of the quantum spin Hall effect. The new state has been generalized from two dimensions to three dimensions and one dimension, from insulator to superconductors, semimetals and other systems such as photonic crystals, metamaterials and even classical mechanics.
In this talk I first present an introduction to topological phases of matter and recent progresses especially on topological superconductors and topological Weyl semimetal. A simple but unified description for a large family of topological phases of matter based is presented based on a modified Dirac equation.