• Thouless pumps and winding invariant

  • Thouless pumps
  • Hamiltonians with parameters
  • Quantum pumps
  • Quantization of pumped charge
  • Counting electrons through reflection
  • Applying the topological invariant
  • Quantized charge and scattering invariant

• Quantum Hall effect: pumping electrons in Landau levels

  • Introduction to Quantum Hall effect: pumping electrons in Landau levels
  • The Hall effect
  • The classical Hall effect is a linear effect
  • The quantum Hall effect: experimental data
  • Quantized Hall conductance from pumping: Laughlin argument
  • Landau levels: a microscopic model for the quantum hall effect
  • Flux pumping of electrons in a Hall cylinder
  • Conclusion: Quantum Hall effect: pumping electrons in Landau levels

• Quantum Hall effect: edge states

  • Where do the pumped electrons come from and go to?
  • A closer look at the chiral edge states
  • The harmless anomaly of the chiral edges
  • Quantization of Hall Conductance from edge states
  • Important things to know about edge states