Topology in condensed matter systems

Instructor:
張明哲 

Reference: Topological Insulators and Topological Superconductors, by B.A. Bernevig (2013)

Grading: Homework (60%); term report (40%)

TA:

Required background: Quantum mechanics, solid state physics

 

        00 Some topology

        01 Review of Bloch theory
        02 Review of Berry Phase
        03 Berry curvature of Bloch states

        04 Quantum anomalous Hall effect

        05 Topological insulator

        06 Point degeneracy between energy bands

        07 Weyl semi-metal

        08 Electromagnetic response of Weyl semi-metal

        09 Review of BCS theory

        10 1D p-wave superconductor

        A longer list

 

Some Review of Modern Physics papers

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

Anomalous Hall effect , by N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, and N.P. Ong, Rev. Mod. Phys. 82, 1539 (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).

Classification of topological quantum matter with symmetries, by Ching-Kai Chiu, Jeffrey C. Y. Teo, Andreas P. Schnyder, and Shinsei Ryu, Rev. Mod. Phys. 88, 035005 (2016).

Weyl and Dirac semimetals in three-dimensional solids, N. P. Armitage, E. J. Mele, and Ashvin Vishwanath, Rev. Mod. Phys. 90 015001 (2018).

Topological photonics, Tomoki Ozawa, Hannah M. Price, Alberto Amo, Nathan Goldman, Mohammad Hafezi, Ling Lu, Mikael C. Rechtsman, David Schuster, Jonathan Simon, Oded Zilberberg, and Iacopo Carusotto, Rev. Mod. Phys. 91 015006 (2019).

Topological bands for ultracold atoms, N. R. Cooper, J. Dalibard, and I. B. Spielman, Rev. Mod. Phys. 91 015005 (2019).

Experimental perspective on three-dimensional topological semimetals, B. Q. Lv, T. Qian, and H. Ding, Rev. Mod. Phys. 93 025002 (2021).

Exceptional topology of non-Hermitian systems, Emil J. Bergholtz, Jan Carl Budich, and Flore K. Kunst, Rev. Mod. Phys. 93 015005 (2021).

Quantum anomalous Hall effect , C. Z. Chang, C. X. Liu, and A. H. MacDonald, Rev. Mod. Phys. 95 011002 (2023).