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 language | English |
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Pages (from-to) | 1301-1311 |
Number of pages | 11 |
Journal | Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties |
Volume | 77 |
Issue number | 5 |
DOIs | |
State | Published - May 1998 |
Externally published | Yes |