Topology in condensed matter systems 

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

 

        01 Basics of differential topology

        02 Review of Berry phase

        03 Berrycurvature of Bloch state

        04 Modern theory of charge polarization

        05 Quantum Hall effect

        06 Quantum anomalous Hall effect

        07 Two dimensional material

        08 Topological insulator

        09 Surface state of topological insulator

        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).

Topological phases in polar oxide nanostructures , J. Junquera et al, Rev. Mod. Phys. 96 021002 (2024).

Topologically protected transport in engineered mechanical systems , T. Shah, C. Brendel, V. Peano, and F. Marquardt Rev. Mod. Phys. 96 021002 (2024).