1. Topological states of matter – from the quantum Hall effect to Majorana fermions
Ady Stern
(Weizmann)
The quantum Hall effects – introduction
Unavoidable conclusions

2. The quantum Hall effects
Introduction

3. Landau level filling factor = density of electrons
The Hall effect I B
Electrons in two dimensions
Classically,
Hall resistivity
longitudinal resistivity - unchanged by B.
Quantum mechanically
degenerate harmonic oscillator spectrum
Landau levels
Landau level filling factor =
density of electrons
density of flux quanta

4. The quantum Hall effect
zero longitudinal resistivity - no dissipation
quantized Hall resistivity to amazing precision
Integer quantum Hall effect - integer n
Fractional quantum Hall effect

5. Single particle spectrum – highly degenerate Landau levels

6. The original sample of the FQHE: