PPT-Topological Band Theory I. Introduction

Insulating State Topology and Band Theory II Band Topology in One Dimension Berry phase and electric polarization Su Schrieffer Heeger model domain wall states and . . Yukio Tanaka (Nagoya University). http://www.topological-qp.jp/english/index.html. Chernogolovka. . . June . 17 (2012). Main collaborators. Theory . Y. Asano . （. Hokkaido. ）. A. Golubov (Enshede). ISSP, The University of Tokyo, Masatoshi Sato. 2. 3. Outline. . What is topological superconductor. T. opological superconductors in various systems. 4. What is topological superconductor ?. Topological superconductors . 13th May 2005 Solar Flare. William M.R. Simpson, Angela Des . Jardins. University of St. Andrews, Montana State University. Contact. :. Email:. www. : . William M. R. Simpson. wmrs2@st-and.ac.uk. http://solar.physics.montana.edu/home/www/REU/2009/wsimpson . Topological Insulators. No conduction through. . interior of material. Current flows along . surfaces,. not terribly sensitive . to . defects. With spin-orbit . interaction, . similar to intrinsic . “Topologically . Robust Transport of Photons in a Synthetic Gauge Field. ," S. Mittal, J. Fan, S. . Faez. , A. . Migdall. , J.M. Taylor, M. . Hafezi. , Phys. Rev. . Lett. ., 113, 087403 (2014. ). Topological transport of light is the photonic analog of topological electron flow in certain semiconductors. In the electron case, the current flows around the edge of the material but not through the bulk. It is “topological” in that even if electrons encounter impurities in the material the electrons will continue to flow without losing energy. Not continuously deformable. Topological. Invariant. Topology & Topological Invariant. Number of Holes. Manifold . of wave functions in the . Hilbert space . r. xy. r. xx. Quantum Hall system:. D. Hilbert. Weisong. . Tu. Department of Physics and Astronomy. University of Tennessee. Instructor: Dr. . George . Siopsis. Introduction. Quantum Hall Effect. The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields. In the quantum hall effect, and the conductivity can be represented as. Symmetry. Topology. Interplay between symmetry and topology has led to a new understanding of . electronic phases of matter.. Conceptual simplification. Conservation laws. Distinguish phases of matter. Dimitrie Culcer. D. Culcer, PRB 84, 235411 (2011). . D. Culcer, . Physica. E 44, 860 (2012) – review on TI transport . Outline. Introduction to topological insulators. . and. . Topological. . phases. . of. matter. b. y. Reichmann Alexander. Overview. Phase . transitions. Topology. Quantum Hall . effect. Superconductivity. Applications. Phase . transition. Different . Hafezi. , S. Mittal, J. Fan, A. . Migdall. , J.M. Taylor, Nature Photonics, . (. 2013. ) . doi:10.1038/nphoton.2013.274. . Topology . -- the understanding of how things are connected -- remains abstract, even with the popular example of doughnuts and coffee cups. This concept, esoteric as it appears, is also neat because it is the basis for creating . . Cumrun Vafa. . Oct. 31, 2017. . 20 . Years . Later: The Many Faces of . AdS. /CFT. Princeton University. Girish S . Setlur. Department of Physics. IIT Guwahati. COPYRIGHT DISCLAIMER: . ALL ILLUSTRATIONS . AND SOME PASSAGES IN . THESE SLIDES HAVE BEEN DOWNLOADED FROM VARIOUS INTERNET SOURCES.. LISTING EACH SOURCE SEPARATELY WILL TAKE UP ALL MY TIME SO I SHALL DESIST FROM DOING SO.. Takehito. Yokoyama, Yukio Tanaka. *. , and Naoto . Nagaosa. Department of Applied Physics, University of . Tokyo, Japan. *. Department . of Applied Physics, Nagoya . University, . Japan. arXiv:0907.2810.