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

The divergent at omega = 0 quantum correction to conductivity delta sigma(2)(omega) of the leading order in (k(F)l)(-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 (k(F)l)(-1). More subtle treatment of the problem shows that delta sigma(2)(omega) is non-zero due to ballistic contributions neglected previously. Knowledge of delta sigma(2)(omega) allows to estimate value of the so-called unitary localization length as (zeta) over bar (u) approximate to lexp(1.6g(2)) where Drude conductivity is given by sigma(0) =ge(2)/h. This estimation underpins the statement of the linear growth of sigma(xx) 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. (C) 2009 Elsevier B.V. All rights reserved.