Topological quantum numbers in condensed matter systems

Where: HIT F11.1

When: Thu 12:45-15:30 (V+U)

Tentative syllabus.


  • Lecture 1, 19.02.2015
    Introduction (pdf) and
    Quantum Hall Effect I (phenomenology) (pdf).
  • Lecture 2, 26.02.2015
    Scaling theory of localization (pdf) and
    Quantum Hall Effect II (topology) (pdf).
  • Lecture 3, 12.03.2015
    Chern insulators (pdf) and
    Topological insulators (pdf).
  • Lecture 4, 19.03.2015
    Topological insulators I (pdf).
  • Lecture 5, 26.03.2015
    Topological insulators II (pdf).
  • Lecture 6, 16.04.2015
    Significant others (pdf).
  • Lecture 7, 23.04.2015
    Fractional quantum Hall effect I (pdf).
  • Lecture 8, 07.05.2015
    Composite fermions (partially incomplete pdf).



[1] A. Altland and B. Simons, Condensed Matter Field Theory (Oxford University Press, 2010), second edition ed.
[2] J. E. Avron and R. Seiler, Quantization of the Hall Conductance for General, Multiparticle Schrödinger Hamiltonians, Phys. Rev. Lett. 54, 259 (1985).
[3] G. V. Dunne, Aspects of Chern-Simons Theory, in [12], chap. 3, p. 177.
[4] T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).
[5] S. M. Girvin, The Quantum Hall Effect: Novel Excitations and Broken Symmetries, in [12], chap. 2, p. 53.
[6] B. I. Halperin, Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B 25, 2185 (1982).
[7] T. Ihn, Semiconductor Nanostructures (Oxford University Press, 2011).
[8] M. Kohmoto, Topological invariant and the quantization of the Hall conductance, Ann. Phys. (NY) 160, 343 (1985).
[9] R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B 23, 5632 (1981).
[10] D. J. Thouless, M. Kohmoto, M. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405 (1982).
[11] X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press, 2004).
[12] A. Comtet, T. Jolicoeur, S. Ouvry, and F. David, eds., Topological aspects of low dimensional systems (Springer-Verlag, Berlin, 1999).
[13] A. Kitaev, Lecture notes on: Topological Quantum Systems URL
[14] B. A. Bernevig, Topological insulators and topological superconductors (Princeton University Press 2013)
[15] E. Fradkin, Field Theories of Condensed Matter Physics (Cambridge University Press 2013)