Topology in condensed matter systems
Instructor: 張明哲
Main
reference: Topological
Insulators and Topological Superconductors, by B.A. Bernevig (2013)
Grading: Homework (70%); term
report (30%)
Required
background: Quantum
mechanics, solid state physics
Introduction:
Topological
Insulators, by C. Kane and J.E. Moore, Physics World 24, 32 (2011).
Some
history, a ppt
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
08 Effective
Hamiltonian of topological insulator
09 Electromagnetic
response of surface states
10 More about 4 by
4 Hamiltonian matrix (optional, except Subsec.A)
11 Dimensional
reduction (optional)
Files
in 1 Periodic table ppt
Second
semester
12 Point
degeneracy between energy bands
13 Weyl semi-metal
14 Electromagnetic
response of Weyl semi-metal
18 Superconductor
pairing with spin
19 Topological
superconductor with time-reversal symmetry
20
22
Periodic table: Dirac Hamiltonian representative
App.
Files
in 1
References:
lecture notes
An
introduction to topological phases of electrons, by J. Moore at UC Berkeley
Les Houches:
Topological aspects of condensed matter physics, 2014
Boulder school
for condensed matter and materials physics, 2016
books
Geometrical
Methods of Mathematical Physics, by B.F. Schutz (1980)
Geometry,
Topology and Physics, 2nd ed, by M. Nakahara (2003)
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)
Berry
Phases in Electronic Structure Theory: Electric Polarization, Orbital
Magnetization and Topological Insulators, by David Vanderbilt (2018).
Ьр①Жロю絶縁体・超伝導体, by 野村 健太郎 (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)
Topology and
Quantum Phases of Matter (Kickoff Workshop, Aug 2018)
special topics
nodal material
Dirac
materials, by T.O. Wehling, A.M. Black-Schaffer, and A.V.Balatsky, Advances
in Physics, 63, 1, (2014).
Weyl
and Dirac semimetals in three-dimensional solids, by N.P. Armitage, E.J.
Mele, and Ashvin Vishwanath, Rev Mod Phys, 90, 015001 (2018)
topological superconductor
Non-Abelian
anyons and topological quantum computation, by Chetan Nayak,
Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma,
Rev. Mod. Phys. 80, 1083 (2008).
Random-matrix
theory of Majorana fermions and topological superconductors, by C.W.J.
Beenakker, Rev. Mod. Phys. 87, 1037 (2015).
interacting system
Zoo
of quantum-topological phases of matter, by Xiao-Gang Wen, Rev. Mod. Phys,
89, 041004 (2017).
Interacting
Topological Insulators: a review, by Stephan Rachel,
arXiv:1804.10656.
topological photonics
Quantum
spin Hall effect of light, K. Y. Bliokh, D. Smirnova, and F. Nori, Science
348, 1448 (2015).
Topological Photonics,
Ozawa et al, arxiv: 1802.04173.
more links
http://web.mit.edu/redingtn/www/netadv/Xtopolinsu.html