Topology in condensed matter systems

Instructor: 張明哲 

Textbook: Topological Insulators and Topological Superconductors, by B.A. Bernevig

Grading: Homework (%60); written and oral report (%40)

Required background: Quantum mechanics, solid state physics

TA: 陳俊明

Outline:

Two major pillars of this course are quantum Hall system and topological insulator.

We will focus on non-interacting systems in the first semester, electron interaction may be discussed

to some extent in the second semester. This course is for students highly interested in the theory of

condensed matter systems with non-trivial topologies.

　

References:

    introductory articles

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

    books

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

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

    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)

    lecture notes

        Geometry and topology in many-particle physics, by J. Moore at UC Berkeley

        Special Topics in Quantum Information Processing, by A.J. Leggett at U. Waterloo

        トポロジカル絶縁体, by 野村健太郎 at 東北大学

    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

 

Topics to be covered:

        01 Bloch band theory
        02 Berry Phase
        03 Integer quantum Hall effect
        04 Time Reversal Symmetry
        05 Magnetic Field on the Square Lattice
        06 The Bulk Edge Correspondence
        07 Graphene
        08 Simple Models for the Chern Insulator
        09 Time Reversal Invariant Topological Insulators
        10 Z2 Invariants
        11 Crossings in Different Dimensions
        12 Time Reversal Topological Insulators with Inversion Symmetry
        13 Quantum Hall Effect and Chern Insulators in Higher Dimensions
        14 Dimensional Reduction of 4D Chern Insulators to 3D Time Reversal Insulators
        15 Experimental Consequences of the Z2 Topological Invariant
        16 Topological Superconductors in One and Two Dimensions
        17 Time Reversal Invariant Topological Superconductors
        18 Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces