Simulation: powers combined¶
Are you tired yet of all the different kinds of topology? If no, this assignment is for you :-)
By now you should have a feel for how to make new topological phases. Your task now is to combine the two systems you’ve learned about and to create a Floquet crystalline topological insulator. If you want even more challenge, create also a gapless Floquet topological material.
Take care however: if you take a topologically nontrivial system and just apply rapid driving, you’ll still get a topological one. This cheating way is prohibited: at any moment during the driving cycle the Hamiltonian of your system should remain gapped.
Now share your results:
Review assignment¶
Kitagawa et al. (2010)¶
Hint: Computes topological edge states from Floquet Hamiltonian.
Rudner et al. (2012)¶
Hint: Points out and explains why the floquet Hamiltonian in momentum space does not capture the presence of Floquet edge states.
Hsieh et al. (2012)¶
Hint: Theoretical prediction of topological crystalline insulator.
Fulga et al. (2012)¶
Hint: Are topological crystalline surface states stable against disorder?
Bonus: Find your own paper to review!¶
Do you know of another paper that fits into the topics of this week, and you think is good? Then you can get bonus points by reviewing that paper instead!
- Kitagawa, T., Berg, E., Rudner, M., & Demler, E. (2010). Topological characterization of periodically-driven quantum systems. 10.48550/ARXIV.1010.6126
- Rudner, M. S., Lindner, N. H., Berg, E., & Levin, M. (2012). Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems. 10.48550/ARXIV.1212.3324
- Hsieh, T. H., Lin, H., Liu, J., Duan, W., Bansil, A., & Fu, L. (2012). Topological Crystalline Insulators in the SnTe Material Class. 10.48550/ARXIV.1202.1003
- Fulga, I. C., van Heck, B., Edge, J. M., & Akhmerov, A. R. (2012). Statistical Topological Insulators. 10.48550/ARXIV.1212.6191