Statistics of conductances and subleading corrections to scaling near the integer quantum Hall plateau transition

¹ Institut für Nanotechnologie, Karlsruhe Institute of Technology (KIT) - 76021 Karlsruhe, Germany
² Department of Applied Physics, Hokkaido University - Sapporo 060-8628, Japan
³ Institut Néel, CNRS and Université Joseph Fourier - 38042 Grenoble, France
⁴ Department of Physics, University of California - Santa Barbara, CA 93106, USA
⁵ Department of Physics, The Ohio State University - 191 W. Woodruff Ave., Columbus, OH 43210, USA
⁶ Institut für Theorie der Kondensierten Materie, Karlsruhe Institite of Technology (KIT) - 76128 Karlsruhe, Germany
⁷ DFG-Center for Functional Nanostructures, Karlsruhe Institite of Technology (KIT) - 76131 Karlsruhe, Germany

Received: 27 June 2013
Accepted: 21 October 2013

Abstract

We study the critical behavior near the integer quantum Hall plateau transition by focusing on the multifractal (MF) exponents X_q describing the scaling of the disorder-average moments of the point contact conductance T between two points of the sample, within the Chalker-Coddington network model. Past analytical work has related the exponents X_q to the MF exponents of the local density of states (LDOS). To verify this relation, we numerically determine the exponents X_q with high accuracy. We thereby provide, at the same time, independent numerical results for the MF exponents for the LDOS. The presence of subleading corrections to scaling makes such determination directly from scaling of the moments of T virtually impossible. We overcome this difficulty by using two recent advances. First, we construct pure scaling operators for the moments of T which have precisely the same leading scaling behavior, but no subleading contributions. Secondly, we take into account corrections to scaling from irrelevant (in the renormalization group sense) scaling fields by employing a numerical technique (“stability map”) recently developed by us. We thereby numerically confirm the relation between the two sets of exponents, X_q (point contact conductances) and (LDOS), and also determine the leading irrelevant (corrections to scaling) exponent y as well as other subleading exponents. Our results suggest a way to access multifractality in an experimental setting.