Quantum percolation and plateau transitions in the quantum Hall effect

Journal Article · Mon Jun 28 00:00:00 EDT 1993 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.70.4130· OSTI ID:6184364

Lee, D; Wang, Z; Kivelson, S ^[1]

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1. IBM Research Division, Thomas J. Watson Research Center, Yorktown Heights, New York 10598 (United States) Center for Materials Science and Theoretical Division T-11, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Department of Physics, University of California at Los Angeles, Los Angeles, California 90024-1547 (United States)

We introduce a simple model of quantum percolation and analyze it numerically using transfer matrix methods. A central point of this paper is that 3 both integer and fractional plateau transitions in the quantum Hall effect are due to quantum percolation. Within this model, we obtained the localization length exponent [nu]=2.4[plus minus]0.2, the dynamical exponent [ital z]=1, and the scaling functions for the conductivity tensor for both the integer and the fractional transitions. We show that our results agree extremely well with the experimental results for the integer plateau transition obtained by McEuen [ital et] [ital al].

• OSTI ID: 6184364
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 70:26; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

665430* -- Other Topics in Quantum Fluids & Solids-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CALCULATION METHODS
HALL EFFECT
MATHEMATICS
NUMERICAL ANALYSIS
QUANTIZATION
SCALING LAWS
TRANSFER MATRIX METHOD
TRANSPORT THEORY
TUNNELING