Is the peak value of σ _xx at the quantum Hall transition universal?

Abstract

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance g is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity σ _xx was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that σ _xx is reduced by a factor (1 + g/2π)⁻¹, at least for small g. This provides some theoretical evidence for the non-universality of σ _xx , as observed in a number of experiments.