Dear reader,

Here are some topics that interest or interested me at some point and a list to some literature.

Topological Insulators

• Hasan, M. Zahid, and Charles L. Kane. "Colloquium: topological insulators." Reviews of modern physics 82.4 (2010): 3045. (arXiv:1002.3895) A review article by some of the early pioneers of this field. A good place to start before delving into more contemporary or detailed papers.
• Qi, Xiao-Liang, and Shou-Cheng Zhang. "Topological insulators and superconductors." Reviews of Modern Physics83.4 (2011): 1057. (arXiv:1008.2026) A review article by some of the early pioneers of this field. A good place to start before delving into more contemporary or detailed papers.
• Qi, Xiao-Liang, Taylor L. Hughes, and Shou-Cheng Zhang. "Topological field theory of time-reversal invariant insulators." Physical Review B 78.19 (2008): 195424. (arXiv:0802.3537) A bit lengthy but full of many nice ideas.
• Bernevig, B. Andrei, Taylor L. Hughes, and Shou-Cheng Zhang. "Quantum spin Hall effect and topological phase transition in HgTe quantum wells." Science 314.5806 (2006): 1757-1761. (cond-mat/0611399) A proposal for the realization of the Quantum Spin Hall Effect.
• König, Markus, et al. "Quantum spin Hall insulator state in HgTe quantum wells." Science 318.5851 (2007): 766-770. (arXiv:0710.0582) A realization of the previous proposal.

There are many, many papers on similar topics that are worth reading. However, these are good places to start from. Explore the references they cite.

Here are some books to complement the journal articles.

• Károly, Asbóth János. A Short Course on Topological Insulators: Band-structure Topology and Edge States in One and Two Dimensions. Springer, 2016. Not very heavy on the math so it's a good place to start for someone completely new to the field.
• Bernevig, B. Andrei, and Taylor L. Hughes. Topological Insulators and Topological Superconductors. Princeton University Press, 2013. A lot of typos. The topics are nice, but the presentation is not as pedagogical as it could be. Might be useful to read this book and understand as a much as you can and then find other references for the topics it mentions.
• Shun-Qing, Shen. Topological Insulators: Dirac Equation in Condensed Matter. Springer, 2018. Something like a textbook and a reference. Could be useful to some.
• Vanderbilt, David. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators. Cambridge University Press, 2018. A book by one of the people who contributed a lot to the understanding of geometric phases in materials.