Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan (Dated: December 15, 2018) Contents I. E ective Hamiltonian of topological insulator 1 A. E ective Hamiltonian of bulk states1 B. E ective Hamiltonian of TI surface states2 C. Berry curvature near level crossing3 1.

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These lecture notes Our aim with this set of lecture notes is to complement the literature cited above: we wish to provide a close look at some of the core concepts of topological insula-tors with as simple mathematical tools as possible. Using one-and two-dimensional noninteracting lattice models, we explain what edge states and what bulk topolog-.

Read Article →Introductory lecture on. topological insulators. Reza Asgari. Workshop on graphene and topological insulators, IPM. 19- 20 Oct. 2011.

Read Article →Examination: homework problems on part 1, project based on one of the guest lectures. Lecture notes downloadable from the course homepage.. topological insulators, Chern insulators, topological superconductors,. Groundstate degeneracies on higher-.

Read Article →Lecture 1 and 2: Introduction (mostly about topological insulators). Dirac equation. Jackiw-Rebbi solution. Quadratic correction to the Dirac equation. Skyrmions. Zero-energy boundary solutions. The slides from my introductory lecture are available here, with my lecture notes here. My notes follow the first chapter in Shun-Qing Shen's book.

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Lecture Topics: 1. Topological Band Insulators (mostly 1D) 2. Topological Insulators (2D and 3D) 3. Low energy models for real materials 4. Wannier representations and band projectors.

In condensed matter physics, complex order often emerges from simple interactions. Recent experiments show that topological order, previously seen only in 2D electron systems in high magnetic field, can exist in zero field and even in bulk 3D materials called topological insulators, in which spin-orbit coupling induces the topological order.

B. Andrei Bernevig with Taylor L. Hughes, Topological Insulators and Topological Superconductors, Princeton University Press (2013). John Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics, Cambridge University Press (1996).

In this article, we will give a brief introduction to the topological insulators. We will briefly review some of the recent progresses, from both theoretical and experimental sides.

III. Topological Insulators in 3D - Weak vs strong - Topological invariants from band structure IV. The surface of a topological insulator - Dirac Fermions - Absence of backscattering and localization - Quantum Hall effect - qterm and topological magnetoelectric effect - Surface topological order Lecture notes available at.

A topological insulator is a material that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material. Topological insulators have non-trivial symmetry-protected topological order; however, having a conducting surface is not unique to topological insulators, since ordinary band insulators can also.

Topological phases of quantum matter comprise a vibrant research area in condensed matter physics. The field originated with the discovery and explanation of quantum Hall effects in the early 1980s but has since vastly expanded to include topological insulators and superconductors, quantum spin liquids, topological semimetals, and more.

Read Article →Topological Physics in Band Insulators II. The canonical list of electric forms of matter is actually incomplete Conductor Insulator Superconductor. as a transition in the ground state topology. Summary of Second Lecture: This transition occurs at the boundary between a topological insulator and an ordinary insulator.

Read Article →Excitations in magnets; solitons and quasiparticles. Landau levels. Magnetic Materials and Magnetic interactions, in insulators and conductors. Brief notes on Nuclear spins and NMR. (2) Hubbard and Anderson Models: Basic description of a lattice of ions. The conducting regime, the insulating regime, and the metal-insulator transition.

Read Article →We will discuss graphene, topological insulators, superfluidity and superconductivity, magnetism, and other subjects as time permits There will be no required text for this course, but we will use last quarter's text from 123A, The Oxford Solid State Basics by Steve Simon, sometimes for reference.

Read Article →*Materials that conduct heat or electricity are known as conductors. Materials that do not conduct heat or electricity are known as insulators. Insulators and conductors have many useful functions.*

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Thermal insulation consists of materials that conduct heat poorly. There is no perfect insulator, but a thin layer of air resists the flow of heat about 15,000 times better than a good metallic conductor of the same thickness. Many good insulators are made of nonmetallic materials filled with tiny air spaces.