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Here is the lecture notes on TI, which is partly based on the lecture notes given by Janos Asboth, Laszlo Oroszlany, and Andras Palyi, Here is the resource, and you can also download a copy here. Other good Books and review papers on this subject:
More geometrical staffs at this one Geometry, Topology and Physics, by Nakahara. Built with Sphinx using a theme provided by Read the Docs.
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. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems. 2D Materials Egde and Boundary States Quantum Hall Insulators SSH Model of Topological Insulators Time-reversal Symmetry Topological Insulators Explained Topological Insulators Textbook
Download PDF Abstract: 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 band insulators in one and two dimensions. 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. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems. From: János K. Asbóth [view email]
Hand written notes: Classes 1-6Download Hand written notes: Class 7Download Hand written notes: Class 8Download Slides: Intro and experimentsDownload Typed notes: complete up to 3D-TIsDownload Video Lessons: Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 (first hour missing, sorry!), Lecture 6, Lecture 7, Lecture 8 General reviews: Books
Chapter 1: Basics and Symmetries Tight-Binding in 2nd quantization notes*Download (*) I am not sure who is the author of these notes, please contact me if you see this, and I will give you credit. Chapter 2: Examples of 1D topological phases: SSH, Rice-Mele and Kitaev wire
Chapter 3: Chern insulators and Quantum Spin-Hall insulators
Chapter 4: 3D Time-reversal invariant topological insulators in class AIII
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