1. Ballistic transport under Quantum Hall effect conditions Ballistic transport under Quantum Hall effect conditions S.Nazin, V.Shikin, ISSP RAS S.Nazin, V.Shikin, ISSP RAS

2. Outline 1. 1-D ballistic conductance definition 1. 1-D ballistic conductance definition 2. Hall-effect, Quantum Hall-effect (QHE) definitions 2. Hall-effect, Quantum Hall-effect (QHE) definitions 3. Edge (ballistic) scenario for QHE realization (Halperin, 1982; Buttiker, 1986) 3. Edge (ballistic) scenario for QHE realization (Halperin, 1982; Buttiker, 1986) 4. Technical service for Halperin-Buttiker scenario. 4. Technical service for Halperin-Buttiker scenario. 5. Resume. 5. Resume.

3. 1-D channel ballistic coductance.

4. Narrow 1-D channel definition

5. Conductance G(V)

6. 2D Hall-bar setup

9. Shub-de-Haas oscillations and the Hall resistance for 1-D ballistic channel.

11. Conventional skipping states in magnetic field

12. Data: Phys.Rev B 38, 3625

13. B.I.Shklovskii et al., Phys. Rev. B46 (1992) p.4026

14. 1-D channel electrostatics

15. The corresponding density profile n(x) and the $x_l$ - point positions definition

16. H=1.02………………….H=1.05

18. Resume: 1. Self consistent description of 1-D channel ballistic conductance under QHE conditions is presented. 1. Self consistent description of 1-D channel ballistic conductance under QHE conditions is presented. 2. Benefice to B.Shklovski idea 2. Benefice to B.Shklovski idea 2. In general the activity around MES (magnetic edge states) is not so routine. 2. In general the activity around MES (magnetic edge states) is not so routine.

19. External potential, the profile n(x) of electron density, position of static skin- layer and its relative scale

21. QHE without edge states

22. H =0.6

24. Saddle point influence