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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 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 • Motivation • Results • Experiment • Explanation • Outlook
Introduction • Two-dimensional electron gas (2DEG) • applications: • high frequency devices • fundamental research: • Quantum Hall Effect • Weak localization problem
Vxy Vxx Quantum Hall Effect
B 0 Band Structure B = 0
Effect of Disorder (T = 0) • Order • Disorder Filling factor:
Quantum Phase Transition • Takes place at T = 0 • Critical behavior • Localization length • For non-interacting electrons
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 :
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
Introduction (Summary): • Transition between two plateaus is a quantum phase transition • Critical exponent is not universal • Experimental data do not obey “semicircle” law
Different contacts and field polarity • Antisymmetry:
Vxy Vxy Hall Resistance • Same for both field polarities, but PP transitions on different contacts take place at different fields
How to obtain correct data? • Illumination • Averaging data from different contacts and for both field polarities Gradient is 0.25 %
Recovered semicircle • By proper averaging a “semicircle” behavior can be obtained from slightly inhomogeneous sample
Summary • Antisymmetry effect • Explained by density gradient • Criterion for sample selection and reliable temperature range • Semicircle recovered
Outlook • Reliable scaling experiment on plateau-plateau transition • Plateau-insulator transition