1. Lecture 19-20 Quantum Hall effect in 2D electron systems and its interpretation in terms of edge states of Landau levels Two-dimensional electrons in GaAs/AlGaAs heterostructure, or in a Si/SiO 2 field-effect transistor

2. weak magnetic field regime

3. Landau levels for electrons in a magnetic field

4. Edge states of Landau levels and edge currents

5. an ideal ‘ballistic quantum wire‘ filling factor (both spin states are filled int he lowest Landau level)

7. ‘ballistic quantum wire‘ due to edge states: edge current spin degeneracy

8. Quantum resistance standard (1 Klitzing)

9. Integer quantum Hall effect density of states 231 3 1 2 degeneracy factor, g (g=2 for spin) localised states in the 2D bulk, current carried only by edge states current carried by states in the bulk, from one edge to the other

10. n = number of filled spin-polarised Landau levels

11. filling factor ‘relativistic-type’ Landau level spectrum -2-440 n e (10 12 cm -2 ) 2 2 4 6 0  xx (k  )  xy (4e 2 /h) 1 2 -2 -4 0 -3 4 3 magnetic length

12. Graphene synthesised on SiC flake growth and lies as a carpet over SiC substrate. Seyller (Erlangen), Yakimova (Linkoping) Development of QHE resistance standard using SiC-synthesised graphene. Currently: 9 digit accuracy (Chalmers, NPL-UK, Lancaster)

15. Skipping orbits and electron ‘focusing‘ B. van Wees 1989

16. Caustics in the electron skipping motion C. Beenakker, 1992 (theory) B. van Wees (exp)