Tunnelling percolation: Universality and application to the integer quantum Hall effect

Alex Hansen, János Kertész

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

The critical phenomena in the integer quantum Hall effect (IQHE) occurring at half-filling of the Landau levels have been related to classical percolation with the additional quantum effects of tunnelling and interference. Experimental results show that the correlation length exponent VH is larger than the classical percolation exponent Vp roughly by unity. Earlier numerical solutions of the model of the full problem, the Chalker-Coddington model, reproduced this value. By using a scaling argument, Mil’nikov and Sokolov suggested that tunnelling alone leads already to the result VH = Vp+ 1. We have shown by analytical arguments and numerical simulations that this is not the case; quantum tunnelling does not change the universality of classical percolation; thus the observed non-universal exponent should be attributed to interference phenomena. We also predict a cross-over in the IQHE from the quantum to the classical value of the exponent.

Original languageEnglish
Pages (from-to)1301-1311
Number of pages11
JournalPhilosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
Volume77
Issue number5
DOIs
StatePublished - May 1998
Externally publishedYes

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