# Topological Insulators Lecture Notes Homework Meme

**Topology in condensed matter systems****Instructor:**張明哲

**Main reference:** Topological Insulators and Topological Superconductors, by B.A. Bernevig (2013)

**Grading:** Homework (30%); term report (70%)

**Required background: **Quantum mechanics, solid state physics

**(Introduction)**

**First semester**

01 Review of Bloch theory

02 Review of Berry Phase

03 Berry curvature of Bloch states

04 Charge polarization and quantum Hall effect

05 1D spin pump

06 2D topological insulator

07 3D topological insulator

08 Effective Hamiltonian of topological insulator

09 Electromagnetic response of surface states

10 More about 4 by 4 Hamiltonian matrix

11 Dimensional reduction

App.

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**Second semester**

12 Point degeneracy between energy bands

13 Weyl semi-metal

14 Electromagnetic response of Weyl semi-metal

15 Review of BCS theory

16 1D p-wave superconductor

17 2D p-wave superconductor

18 Superconductor pairing with spin

19 Topological superconductor with time-reversal symmetry

20

21 Periodic table: Basics

22 Periodic table: Dirac Hamiltonian representative

App. D, E, F

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**References:**

*introductory** article*

Topological Insulators, by C. Kane and J.E. Moore, Physics World 24, 32 (2011).

*books*

Geometrical Methods of Mathematical Physics, by B.F. Schutz

Topological Insulators: Dirac Equation in Condensed Matters, by S.Q. Shen (2013)

Topological Insulators, Ed M. Franz and L. Molenkamp (2013)

Topological Insulators Fundamentals and Perspectives, by F. Ortman et al (2015)

A Short Course on Topological Insulators, by J. Asboth, L. Oroszlany, and A. Palyi (2016)

Bulk and Boundary Invariants for topological insulators: From K-theory to physics, by E. Prodan and H. Schulz-Baldes (2016)

*review** papers*

Berry phase effects on electronic properties, by D. Xiao, M.C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).

Topological insulators, by M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

Topological insulators and superconductors, by X.L. Qi and S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).

Topological band theory, by A. Bansil, H. Lin and T. Das, Rev. Mod. Phys. 88, 021004 (2016).

* lecture notes*

An introduction to topological phases of electrons, by J. Moore at UC Berkeley

Topological insulator (in Japanese), by K. Nomura at Tohoku Univ.

Les Houches: Topological aspects of condensed matter physics 2014

*special issues*

ComptesRendus Physique

Topological insulators / Topological superconductors (2013)

PhysicaScripta

The Nobel Symposium 156: New forms of matter: topological insulators and superconductors (2015)slides

New J Phys: Focus on

Topological Insulators (2011), Majorana Fermions in Condensed Matter (2014),

Topological Semimetals (2016), Topological Physics (2016)

*talks*

Topological Band Theory and the Quantum Spin Hall Effect, by C. Kane at KITP, Dec 8, 2008

Topological Insulators and Superconductors, by S.C. Zhang at Stanford, Sep 10, 2009

Physics@FOM Veldhoven, by C. Kane, Jan 2012

Topological Insulators and Superconductors (KITP program, Sep 19 - Dec 16, 2011)

*more** links*

http://web.mit.edu/redingtn/www/netadv/Xtopolinsu.html

## Title: A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

Authors:János K. Asbóth, László Oroszlány, András Pályi

(Submitted on 8 Sep 2015)

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.

## Submission history

From: János K. Asbóth [view email]**[v1]**Tue, 8 Sep 2015 09:28:54 GMT (15948kb,D)

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