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Effect of density gradients on magnetotransport of quantum Hall systems

Effect of density gradients on magnetotransport of quantum Hall systems. L. Ponomarenko. Participants:. Anne de Visser and Dennis de Lang A. Pruisken (ITF, UvA) G. Galeev (IRE, Moscow) H. Kunzel (HHIN, Berlin). Outline:. Introduction Quantum Hall Effect Quantum Critical Point

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Effect of density gradients on magnetotransport of quantum Hall systems

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

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

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

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

  5. Vxy Vxx Quantum Hall Effect

  6. B  0 Band Structure B = 0

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

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

  9. Experiment

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

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

  13. Different contacts and field polarity • Antisymmetry:

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

  15. Antisymmetry results from density gradient ! A C B D

  16. Antisymmetry results from density gradient ! A C B D

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

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

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

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

  21. Outlook

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