Europhys. Lett., 69 (4), pp. 602–608 (2005) DOI: 10.1209/epl/i2004-10398-7 EUROPHYSICS LETTERS 15 February 2005 Resistance fluctuations near integer quantum Hall transitions in mesoscopic samples C. Zhou 1 ( ∗ ) and M. Berciu 2 1 Department of Electrical Engineering, Princeton University Princeton, NJ 08544, USA 2 Department of Physics and Astronomy, University of British Columbia Vancouver, BC V6T 1Z1, Canada received 18 November 2004; accepted in final form 20 December 2004 published online 14 January 2005 PACS. 73.23.-b – Electronic transport in mesoscopic systems. PACS. 73.43.-f – Quantum Hall effects. PACS. 71.30.+h – Metal-insulator transitions and other electronic transitions. Abstract. – We perform first-principles simulations to study the resistance fluctuations of mesoscopic samples, near transitions between quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices and calculate the Hall and longi- tudinal resistances using the Landauer formula. Our simulations recapture all the observed experimental features. We then use a generalization of the Landauer-B¨ uttiker model, based on the interplay between tunneling and chiral currents, to explain the three regimes with distinct fluctuations observed, and identify the central regime as the critical region. Although the Integer Quantum Hall Effect (IQHE) is generally well understood, recent experiments on mesoscopic samples [1–3] uncovered unexpected behavior in the seemingly noisy fluctuations of the Hall (R H ) and longitudinal (R L ) resistances. Previously, resistance fluctuations were observed in mesoscopic samples with a phase coherence length larger than the sample size [4–7]; they are totally random, similar to universal conductance fluctuations [8]. In contrast, Peled et al. find [1, 2] that the transition between the n-th and (n + 1)-th IQHE plateaus has three distinct regimes: i) on the high-B side, both R H and R L have large but correlated fluctuations, such that R L + R H = h/ne 2 ; ii) for intermediate B values, R H and R L exhibit uncorrelated fluctuations; and iii) on the low-B side, R H = h/(n + 1)e 2 is quantized while R L fluctuates. For n = 0, regions i) and ii) are replaced by the transition to the insulating phase [1]. Moreover, R L + R H = R 2t holds at all B values [2] (the two-terminal resistance R 2t is defined below). Changing the sign of the magnetic field B →-B also has interesting consequences [3], which we discuss later. In this letter, we explain the physics behind these observations in a unified theory. The relation R L + R H = R 2t was first proposed by Streda et al. [9], while the fluctuations of regime iii) are reminiscent of Jain and Kivelson’s theory on the resistance fluctuations of ( * ) Current address: Oak Ridge National Laboratory - PO Box 2008 MS 6164, Oak Ridge, TN 37831-6164, USA. c  EDP Sciences