Topological Surface States during 20052007 Berkeley Lab
Discovering a 2D Topological Insulator (1988type) in a 2D quantum magnet
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Demonstration of a Fully Bulk Insulating (Intrinsic) Topological Insulator Nature Physics 10, 956 (2014) A very recent achievement of condensed matter physics was the discovery that crystalline solids can be characterized by numbers called topological invariants. A topological invariant is a global property of a crystal and, as a result, it is robust against imperfections of the sample or local perturbations. In addition, a nontrivial topological invariant gives rise to electron states near the surface of the sample, with important consequences for applications. For instance, a topological insulator behaves as an ordinary insulator in the bulk of the sample, but because of the nontrivial topological invariant, it has electron surface states which allow it to conduct electricity on the sample surface. Because the topological invariant is a global property of the system, these surface states are robust against disorder. Despite advances in understanding the physics of topological insulators, progress of making actual devices has been limited by the materials currently available. While many topological insulators have been discovered, few of the materials currently known have a sufficiently low bulk conductivity and other key properties, hindering the proposed applications. More precisely, for the advancement of the field, it is crucial to find materials with a large bulk band gap, a chemical potential in the bulk band gap and furthermore at the energy of the surface Dirac point, and surface states with high mobility. This will allow us to develop technologies that take advantage of the unique quantum phenomena associated with the topological surface states. 

Observation of topological surface state quantum Hall effect in an intrinsic threedimensional topological insulator Y. Xu, I. Miotkowski, C. Liu, J. Tian, H. Nam, N. Alidoust, J. Hu, C.K. Shih, M. Z. Hasan and Y. P. Chen Nature Physics 10, 956 (2014) 

Nature 460, 1101 (2009) 

(a), In the quantum Hall effect, the circular motion of electrons in a magnetic field, B, is interrupted by the sample boundary. At the edge, electrons execute "skipping orbits" as shown, intimately leading to perfect conduction in one direction along the edge. (b), The edge of the "quantum spin Hall effect state" or 2D topological insulator contains leftmoving and rightmoving modes that have opposite spin and are related by timereversal symmetry. This edge can also be viewed as half of a quantum wire, which would have spinup and spindown electrons propagating in both directions. (c), The surface of a 3D topological insulators supports electronic motion in any direction along the surface, but the direction of electron's motion uniquely determines its spin direction and vice versa. The 2D energymomentum relation has a "spinDirac cone" structure but with helical or momentum space chiral spin texture with Berry's phase(spins go around in a closed loop in momentum space). 

The first 3D topological insulator: Bi_{1x}Sb_{x} D. Hsieh, D. Qian, Y. Xia, et al., Nature 452, 970 (2008) D. Hsieh, Y. Xia, L. A. Wray, et al., Science 323, 919 (2009) 

First detection of Z_{2} (symmetry protected) TopologicalOrder: spinmomentum locking of spinhelical Dirac electrons in Bi_{2}Se_{3} and Bi_{2}Te_{3} Y. Xia, D. Qian, L. A. Wray, et al., Nature Physics 5, 398 (2009) D. Hsieh, Y. Xia, D. Qian, et al., Nature 460, 1101 (2009) 

The discoveries of new forms of matter have been so definitive that they are used to name periods in the history of mankind, such as Stone Age, Bronze Age, and Iron Age. Although all matter is composed of component particles, particles can organize in various ways leading to different phases of matter. Finding all possible distinct phases that matter can form and understanding the physics behind each of them are fundamentally important goals in physics research and often lead to new technologies, benefiting our society. A topological phase is an unusual type of crystalline solid, characterized by a nontrivial topological number. This number is a global quantity, which depends on the crystal's bulk electronic wavefunctions. 



Berry's phase and quantization in topological insulators. M. Zahid Hasan Physics 3, 62 (2010) 

Demonstration of a Fully Bulk Insulating (Intrinsic) Topological Insulator 

Observation of topological surface state quantum Hall effect in an intrinsic threedimensional topological insulator. Published in Y. Xu, I. Miotkowski, C. Liu, J. Tian, H. Nam, N. Alidoust, J. Hu, C.K. Shih, M. Z. Hasan and Y. P. Chen, Nature Physics 10, 956 (2014). 