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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. Rashba system3 2. Graphene4 3. Surface state of.

These lecture notes are mainly concerned with how the concept of topological insulators is generalized when interactions are included. More generally, the interplay of symmetry and topology is discussed. Traditionally, phases of matter were distinguished on the basis of symmetry alone.

Introductory lecture on. topological insulators. Reza Asgari. Workshop on graphene and topological insulators, IPM. 19- 20 Oct. 2011. 2. Outlines -Introduction. New phases of materials, Insulators -Theory. quantum Hall effect, edge modes, topological invariance -Conclusion. 3 -In classical world we have solid, liquid and gas phases -In quantum world we have metals, insulators.

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible.

Lecture notes on topological insulators Ming-Che Chang Department of Physics, National Taiwan Normal University, Taipei, Taiwan (Dated: November 23, 2018) Contents I. 2D Topological insulator 1 A. General theory1 1. Edge state in 2D topological insulator2 2. Lattice with inversion symmetry2 3. Z 2 integer as a topological invariant3 B. Bernevig-Hughes-Zhang model3 1. Time reversal and space.

Homework problems. For grade 4 or 5: a supplementary oral exam. Schedule please click here Suggested reading Week 1: Quantum Hall effect My lectures this first week followed Secs. 2 and 3.1 in Mark Goerbig, Quantum Hall Effects. rather closely. Goerbig's review contains a lot of information. Use your lecture notes as a guide to what to focus on! Also, read the introductory Sec. 1! For some (by.

This chapter indicates the placing of lecture notes on the subject of topological insulators and superconductors by Shoucheng Zhang from Stanford University. The lecture notes were not supplied for the text so do not appear here. Keywords: topical insulators, superconductors.

This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.

Note that the gapless surface states of topological insulators differ from those in the quantum Hall effect: the gapless surface states of topological insulators are symmetry-protected (i.e., not topological), while the gapless surface states in quantum Hall effect are topological (i.e., robust against any local perturbations that can break all the symmetries).

This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport.

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).

Slides for Lecture 1 (pdf); Homework. Lecture 2 on Majorana fermion experiments (video) Complete list of lecture videos and notes. Introduction to Solid State Physics (Fall 2015) This is an upper-level undergraduate course that follows Steve Simon’s textbook “Oxford Solid State Basics” to go through the early theories of solid state, the 1D toy models and then on to the band theory of.

They are aimed at beginning graduate students. The lecture notes are long (around 400 pages), but bite-sized chunks can be downloaded below. PostScript PDF Content. 1. Topics in Electromagnetism: PDF Introduction; Magnetic monopoles, Dirac quantisation; The theta term, Topological insulators, The Witten effect. 2. Yang-Mills Theory: PDF.

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum.

Topological Aspects of Condensed Matter Physics Lecture Notes of the Les Houches Summer School: Volume 103, August 2014 Edited by Claudio Chamon, Mark O. Goerbig, Roderich Moessner, and Leticia F. Cugliandolo Lecture Notes of the Les Houches Summer School. Presents a modern view on topological matter; Pedagogical presentation.

The basic band structure of a topological insulator is that of a normal insulator, with the Fermi level lying between the conduction and valence bands (see diagram). However, at the surface of the material, there are electron states with energies falling within the bulk energy gap; these are free to move and thus allow conduction. The mechanism behind this phenomenon is very complex, but is.