Topology#
Topological band theory: SSH edge states and the Zak phase, exactly quantized Chern numbers (TKNN), the Haldane model’s zero-net-flux Chern insulator and its chiral edge states, unpaired Majorana zero modes in the Kitaev chain, graphene’s massless Dirac cone, and the Kane-Mele/BHZ \(\mathbb{Z}_2\) topological insulators.
The 3D Topological Insulator: A Single Surface Dirac Cone
The TKNN Invariant: Exactly Quantized Chern Numbers
Graphene: A Massless Dirac Cone on a Honeycomb Lattice
Graphene: Zero-Energy Edge States on a Zigzag-Terminated Flake
The Haldane Model: a Chiral Edge State on an Arbitrary Boundary
The Haldane Model: A Chern Insulator with Zero Net Flux
The Integer Quantum Hall Effect: Quantized Hall Conductance from Chern Numbers
Kane-Mele: Helical Edge States from Two Time-Reversed Haldane Copies
Quantum Spin Hall Effect: Konig et al.’s Helical Edge States
The SSH Model: Zak Phase and Protected Edge States
The Tenfold Way: Three Topological Invariants, One Classification Scheme
Weyl Semimetals: Momentum-Space Monopoles and Fermi Arcs
