COMOP2003 gradient

Quantum Hall effect:antisymmetry in magnetoresistance due to gradient in electron density: 

Quantum Hall effect: antisymmetry in magnetoresistance due to gradient in electron density L. A. Ponomarenko1, D. T. N. de Lang1, A. de Visser1, A. M. M. Pruisken2, V. A. Kulbachinskii3, G. B. Galiev4 and H. Künzel5 1Van der Waals-Zeeman Institute, Univ. of Amsterdam, 1018 XE Amsterdam, The Netherlands 2Institute for Theoretical Physics, Univ. of Amsterdam, 1018 XE Amsterdam, The Netherlands 3Low temperature Physics Department, Moscow State University, 119899 Moscow, Russia 4Institute of Radioengineering and Electronics, RAS, 103907 Moscow, Russia 5Heinrich-Hertz-Institut für Nachrichtentechnik, 10587 Berlin, Germany UNIVERSITEIT VAN AMSTERDAM E-mail: leonidp@science.uva.nl I. Experiment: antisymmetry The longitudinal resistivities measured at both sides of the Hall bar interchange by reversing the polarity of the magnetic field: II. Experiment: density gradient GaAs/AlGaAS quantum well Shift between two curves Rxy(B) measured simultaneously from two pairs of contacts occurs due to gradient in electron density along the Hall bar. III. Explanation of antisymmetry V. Recovered semicircle IV. Flow diagram Illumination by LED increases electron density and makes sample more homogeneous. By applying a proper averaging procedure an almost ideal semicircle can be obtained, when plotting xx vs xy: VI. Outlook Scaling experiments [2] on homogeneous samples. Homogeneous sample require a smallest possible density gradient in which the semicircle can be properly recovered. The influence of macroscopic sample inhomogeneities (density gradient) on critical exponent measured in “traditional” way will be studied both theoretically and experimentally. A phenomenological theory of the Quantum Hall effect based on a local-conductivity approach [1] predicts a universal semicircle relation between the conductivity tensor components xx and xy. References: 1. A. M. Dykhne and I. M. Ruzin, Phys. Rev. B 50, 2369 (1994) 2. H. P. Wei, D. C. Tsui, M. A. Palaanen and A. M. M. Pruisken, Phys. Rev. Lett. 61, 1294 (1988) Abstract. Magnetotransport is the most common method for investigation of the quantum Hall effect. By measuring the longitudinal resistivity xx as a function of magnetic field B for several types of quantum wells and heterostructures in Hall bar geometry, we found: in general, xx(B) curves measured from different pairs of contacts or for both magnetic field polarities are not identical; the longitudinal resistivities measured at both sides of the Hall bar interchange by reversing the polarity of the magnetic field. Such a symmetry can be explained by a small gradient of electron density in the sample. Taking this effect into account is a significant step forwards in the reliable determination of the critical exponent at the plateau-plateau quantum phase transition. I