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

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 upsilon(H) is larger than the classical percolation exponent upsilon(p) 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 upsilon(H) = upsilon(p) + 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.