Topological Insulator: Dirac equation in condensed matter
Affiliation: Hong Kong University
Abstract Details: 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. A topological insulator is characteristic of topological invariant, not the order parameters such as in ferromagnet and superconductors. 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 generalization of this new state from two dimensions to three dimension is non-trivial. In three dimensional topological insulators, the electron momentum in the surface states is locked in with the electron spin and electrons form a Dirac cone due to strong spin orbit coupling. A series of materials such as Bi2Se3 and Bi2Te3 have been verified to be topological insulators. Now we have realized that the topological phase also exists in one-dimensional conducting polymers, and superfluid of Helium 3. In this talk we first present an introduction to topological insulator and then present a simple but unified description for a large family of topological insulators based on a modified Dirac equation. A series of solutions are presented to demonstrate the existence of edge and surface states in topological insulators and superconductors.
About The Speaker: Professor Shun-Qing Shen, an expert in the field of condensed matter physics, is distinguished for his research works on topological insulator, spintronics of semiconductors, quantum magnetism and orbital physics in transition metal oxides, and novel quantum states of condensed matters. He proposed theory of topological Anderson insulator, spin transverse force, resonant spin Hall effect and theory of phase separation in colossal magnetoresistive (CMR) materials. He proved existence of antiferromagnetic long-range order and off-diagonal long-range order in itinerant electron systems. Professor Shen has been a professor of physics at The University of Hong Kong since July 2007. He received his BS (1986), MS (1989), and PhD (1992) from Fudan University in Shanghai. He was a postdoctorial fellow (1992 – 1995) in China Center of Advanced Science and Technology (CCAST), Beijing, Alexander von Humboldt fellow (1995 – 1997) in Max Planck Institute for Physics of Complex Systems, Dresden, Germany, and JSPS research fellow (1997) in Tokyo Institute of Technology, Japan. He was awarded Croucher Senior Research Fellowship (Croucher Prize) in 2010.
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