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.

        Files in 1

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

        Files in 1

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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