• Course plan



    Subject list

    Topic

    Resources 

    Second quantization

    Bruus and Flensberg, "Many-Body Quantum Theory in Condensed Matter Physics: An Introduction "

    Berry phase

    Joel Moore, Les Houches lecture notes;  B. Andrei Bernevig, "Topological insulators and topological superconductors"; Xiao Chang and Niu "Berry Phase Effects on Electronic Properties"

    Topological band theory and electric polarization 

    Xiao Chang and Niu "Berry Phase Effects on Electronic Properties"; David Vanderbilt "Berry phases in electronic structure theory"


    SSH model



     Asboth Oroszlany and Palyi "A Short Course on Topological Insulators"; Franz and Molenkamp "Topological insulators" Chap. 1 (C.  Kane)


    Quantum Hall effect



     David Tong: Lectures on the Quantum Hall Effect; R. B. Laughlin Phys. Rev, B23 5632 (1981); B. I. Halperin Phys. Rev. B25 2185 (1982); Thouless, Kohomoto, Nightingale and den Nijs Phys. Rev. Lett. 49, 405 (1982).

     Graphene 


     Castro Neto et al, Rev. Mod. Phys. 81, 109 2009, B. Andrei Bernevig, "Topological insulators and topological superconductors"

     Chern insulator



     Haldane, F. D. M. Phys. Rev. Lett. 61, 2015 (1988).  B. Andrei Bernevig, "Topological insulators and topological superconductors"


     Topological insulators

     C. L. Kane and E. J. Mele Phys. Rev. Lett. 95, 226801 (2005). Liang Fu and C. L. Kane Phys. Rev. B 74, 195312 (2006)

     The ten fold way




    Shinsei Ryu et al. New J. Phys. 12, 065010 (2010); Jeffrey C. Y. Teo and C. L. Kane Phys. Rev. B 82, 115120 (2010) (Appendix A); Recorded lectures by A. Altland @ https://www.youtube.com/channel/UCmebKVQfI67Z6Y5sa9Iv3xg


     Topological Superconductors


     Last two chapters in  B. Andrei Bernevig, "Topological insulators and topological superconductors" by Taylor Hughes. Jason Alicea 2012 Rep. Prog. Phys. 75 076501


     Weyl Semimetals



     David Vanderbilt "Berry phases in electronic structure theory"Ari M. Turner, Ashvin Vishwanath "Beyond Band Insulators: Topology of Semimetals and Interacting Phases", chapter 11 of  "Topological Insulators" edited by Franz and Molenkamp.




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