Topological Insulator and Topological Superconductor (Rapid Response Program)

Date :From 2011-08-09 To 2011-09-02
Advisory committee :
Local coordinators :Xi Dai (Contact person, Institute of Physics, CAS),Zhong Fang (Institute of Physics, CAS),Jun-Ren Shi (Peking University),Xi Chen(Tsinghua University)
International coordinators :Carlo Beenakker (Leiden University),Laurens Molenkamp (Wuerzburg), Aharon Kapitulnik (Stanford University) Qi-Kun Xue (Tsinghua University),Yue Yu (Institute of Theoretical Physics, CAS)

The Advisory Committee of this program is:

Qian Niu (University of Texas at Austin)

Xin-Cheng Xie (Peking University & Oklahoma State University)

Shou-Cheng Zhang (Chair, Stanford University)

1 Program description:
Since Dirac explicitly involved topology into quantum theory through his work on magnetic monopoles in the 1930s, more and more topological and geometric effects have been predicted and discovered in quantum systems, such as Aharonov–Bohm effect, Berry’s adiabatic phase, geometric structure of gauge theory and so on. In condensed matter physics, there are also many effects that have a topological origin, including quantum Hall (QH) effect, non-Abelian statistics, both of which are not only theoretically but also technologically important.
QH state provided the first example of a quantum state which is topologically distinct from all other states known before. It has a bulk insulating gap and the there is no a spontaneous breaking of any continuous symmetry but there exists a gapless chiral edge states on the boundary. The edge states are determined by the nontrivial global topological properties of the energy level structure in momentum space, which can be characterized by the first Chern number of the induced fiber bundle. Recently, as a generalization, the quantum spin Hall effect and the corresponding state of matter called two-dimensional topological insulators were theoretically predicted and experimentally observed. It is another topologically distinct state of matter, also with bulk gap and stable gapless edge states without any spontaneous breaking of continuous symmetry. Nevertheless, unlike in the QH effect where the magnetic field explicitly breaks the time reversal symmetry, this discrete symmetry plays an essential role in topological insulator, which ensures the Kramers degeneracy of electron states. In particular, the edge states are paired on each edge to form Kramers doublet, which, as a result, move in opposite directions for opposite spins and for the same spin on different edges as well. The discovery of the 2-D topological insulator greatly simulates the study of the topological properties of insulators. Three dimensional topological insulators, which is gapped in bulk and there are topologically protected gapless Dirac type surface states, also have been predicted theoretically and obtained experimentally. Analog to filling factor 5/2 fractional quantum Hall state, the concept of topological superconductors is developed. All these topological states of matter have been classified according to the knowledge of modern topological theory. To search these new states of matter is an important task.  Furthermore, this may realize dissipationless spin current and accumulation which are crucial for spintronics, and thus opens important new possibilities for new quantum devices. With both theoretical interestingness and technological importance, it has produced considerable excitement in the condensed matter community and opened up a new active field of condensed matter physics.
2 Organization Outlines:
The purpose of this program is intended to bring together theorists and experimentalists who work on topological insulator and topological superconductor. It is very timing and necessary to rapidly response this fast developing field. As we know, the same content programs will be run right before and after our proposed time in Apsen center and KITP at Snata Barabra. Therefore, this program will help the condensed matter society in China quickly gets into this research onrush. We shall invite senior scientists working in these areas both inside and outside China as key participants to this program.