How strong is localization in the integer quantum Hall effect: Relevant quantum corrections to conductivity in non-zero magnetic field

The divergent at ω=0 quantum correction to conductivity δσ2(ω) of the leading order in (kFl)-1 has been calculated neglecting Cooperon-type contributions suppressed by moderate or strong magnetic field. In the so-called diffusion approximation this quantity is equal to zero up to the second order in (kFl)-1. More subtle treatment of the problem shows that δσ2(ω) is non-zero due to ballistic contributions neglected previously. Knowledge of δσ2(ω) allows to estimate value of the so-called unitary localization length as ξu≈lexp(1.6g2) where Drude conductivity is given by σ0=ge2/h. This estimation underpins the statement of the linear growth of σxx peaks with Landau level number n in the integer quantum Hall effect regime [1] (Greshnov and Zegrya, 2008; Greshnov et al., 2008) at least for n≤2 and calls Pruisken–Khmelnitskii hypothesis of universality [2] (Levine et al., 1983; Khmelnitskii, 1983) in question.