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Lecture Topics and Background References

Professor M. Zahid Hasan  (Princeton University, USA)
"Topological Insulators and Superconductors: Materials, Models and Experiments”
1. Chern number and Z2 Topological Invariants
2. Quantum Hall effect as a prototype 2D Topological insulator
3. 3D Topological Insulators: theory and experiments
4. Topological Crystalline Insulators
5. Topological Kondo Insulators
6. Topological Dirac Semimetals
7. Topological Quantum Phase Transition
8. Superconductivity in Topological Materials
9. Superconductivity in Dirac systems
10. Majorana Fermion systems

Background References:
"Topological Insulators"
M.Z. Hasan, C.L. Kane; Rev. Mod. Phys 82, 3045 (2010)

"Three-Dimensional Topological Insulators"
M.Z. Hasan, J.E. Moore; Ann. Review. Cond. Mat. Physics 2, 55-78 (2010).
(pedagogical article on quantization) "Topological Quantization in Topological Insulators"
M.Z. Hasan ; Physics 3, 62 (2010).
Dr. Titus Neupert (Princeton Center for Theoretical Science, Princeton University, USA) 
"Classification and axiomatic field theory for topologically ordered phases of matter"
1. Classification of topological phases of matter.
2. Topological superconductors and Kitaev’s 16-fold way.
3. Axiomatic topological quantum field theory: Fusion and braiding categories.
4. Modular matrices and Verlinde’s formula.
5. Anyon condensation.
6. Entanglement entropy and entanglement spectroscopy.

Professor  Nicolas Regnault (Laboratoire Pierre Aigrain, ENS, France)
“Fractional Quantum Hall Effect and Fractional Chern Insulators”
1. The integer quantum Hall effect and Chern Insulators.
2. The fractional quantum Hall effect.
3. Fractional Chern insulators.
4. Strong interactions in C>1 Chern insulators.
5. Fractional topological insulators in 2 dimensions.

Dr. Michael Wimmer  (Delft University of Technology, The Netherlands)
"Quantum Transport in Low-dimensional Topological Materials"
1. Introduction to quantum transport; scattering matrix formalism
2. Quantum Hall effect; Hofstadter butterfly§
3. One-dimensional topological superconductors: Majorana fermions
    * Symmetries and the scattering matrix
    * Topological invariants from the scattering matrix]
    * Engineering topology in hybrid systems
4. Quantum spin Hall effect
    * two-dimensional topological insulators
    * Majorana fermions at the edge
    * Crossover to one dimension

Background References:
[1] S. Datta. Electronic transport in mesoscopic systems. Cambridge
University Press.
[2] J. Asboth, L. Oroszlany, and A. Palyi. Topological insulators.
[3] M. Leijnse, K. Flensberg. Semicond. Sci. Technol. 27, 124003 (2012).
[4] A.R. Akhmerov, J.P. Dahlhaus, F. Hassler, M. Wimmer,
C.W.J. Beenakker. Phys. Rev. Lett. 106, 057001 (2011).
[5] M. Wimmer, A.R. Akhmerov, J.P. Dahlhaus, C.W.J. Beenakker.
New J. Phys. 13, 053016 (2011).
[6] M. Koenig, H. Buhmann, L.W. Molenkamp, T.L. Hughes, C.-X. Liu,
X.-L. Qi, S.-C. Zhang. J. Phys. Soc. Jpn. 77, 031007 (2008).
[7] I. C. Fulga, F. Hassler, A. R. Akhmerov. Phys. Rev. B 85, 165409
[8] I. Adagideli, M. Wimmer, A. Teker. Phys. Rev. B 89, 144506 (2014).
[9] C.W. Groth, M. Wimmer, A.R. Akhmerov, J. Tworzydło,
C.W.J. Beenakker. Phys. Rev. Lett. 103, 196805 (2009).
[10] S. Ryu, A. Schnyder, A. Furusaki, A. Ludwig. New J. Phys. 12,
065010 (2010).
[11] S. Das Sarma, J.D. Sau, T.D. Stanescu. Phys. Rev. B 86, 220506
[12] J. Alicea. Rep. Prog. Phys. 75, 076501 (2012).

I will be using the kwant software package ( It is written in python, so please learn python! This should be very easy for anyone with some programming knowledge. I can recommend as a good source, but searching the internet will give you tons of learning resources.
If you want to prepare very thoroughly for the lecture, I would advise you to learn the concepts of the scattering matrix and quantum transport, as well as tight-binding Hamiltonians (covered for example in [1], but this will also briefly be surveyed in the first lecture). Also, there is an extensive tutorial for the kwant software package on

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