Part I: Basics: Second quantization, Tight binding models of graphene,
Dirac equation in 1D,2D and 3D, Existence of end (1D), edge (2D) and
surface states (3D), Introduction of topological regime in the Dirac
Part II: Topological band theory: Concepts of geometric phase (Berry
phase), the Chern number, Laughlin's guage argument, Hall conductance and
the Chern number, Bulk-edge correspondence, Time reversal symmetry and the
Z-2 invariants Time-reversal invariant topological insulators, Kene-Mele
model and Haldane models, Quantum spin Hall state, Applications to
Topological electronic devices.
Part III: Advanced topics: The Bogoliubov-deGennes formalism for
superconductors, the Kitaev chain and topological superconductivity,
Majorana Fermions and topological quantum computing, device realizations
of Majorana braiding.
Topological Insulators and Topological Superconductors, B. Andrei Bernevig
with Taylor L Hughes, Princeton University Press (2013).
Topological Insulators: The Dirac equation in condensed matter, Shun-Qing
Shen, Springer, (2017).