1. 1 Effect of density gradients on magnetotransport of quantum Hall systems L. Ponomarenko

2. 2 Participants: Anne de Visser and Dennis de Lang A. Pruisken (ITF, UvA) G. Galeev (IRE, Moscow) H. Kunzel (HHIN, Berlin)

3. 3 Outline: Introduction –Quantum Hall Effect –Quantum Critical Point –Motivation Results –Experiment –Explanation Outlook

4. 4 Introduction Two-dimensional electron gas (2DEG) –applications: high frequency devices –fundamental research: Quantum Hall Effect Weak localization problem

5. 5 Quantum Hall Effect V xx V xy

6. 6 Band Structure B  0 B = 0

7. 7 Effect of Disorder (T = 0) Order Disorder Filling factor:

8. 8 Quantum Phase Transition Takes place at T = 0 Critical behavior –Localization length For non-interacting electrons

9. 9 Experiment

10. 10 Criticality InGaAs/InP (H.P.Wei et al., PRL, 1988) –half width of  xx scales as –maximum slope of  xy scales as –  = 0.42 Localization length exponent  and critical exponent  :

11. 11 However… AlGaAs/GaAs –S.Koch et al. (PRB, 1991):  ranges from 0.36 to 0.81 –H.P.Wei et al. (PRB, 1992): scaling only below 0.2 K Semicircle relation

12. 12 Introduction (Summary): Transition between two plateaus is a quantum phase transition Critical exponent is not universal Experimental data do not obey “semicircle” law

13. 13 Different contacts and field polarity Antisymmetry:

14. 14 Hall Resistance Same for both field polarities, but PP transitions on different contacts take place at different fields V xy

15. 15 Antisymmetry results from density gradient ! A BD C

16. 16 Antisymmetry results from density gradient ! A BD C

17. 17 How to obtain correct data? Illumination Averaging data from different contacts and for both field polarities Gradient is 0.25 %

18. 18 Recovered semicircle By proper averaging a “semicircle” behavior can be obtained from slightly inhomogeneous sample

19. 19 Summary Antisymmetry effect Explained by density gradient Criterion for sample selection and reliable temperature range Semicircle recovered

20. 20 Outlook Reliable scaling experiment on plateau-plateau transition Plateau-insulator transition

21. 21 Outlook