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

Abstract

The divergent at ω = 0 quantum correction to conductivity δ σ 2 ( ω ) 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 δ σ 2 ( ω ) is non-zero due to ballistic contributions neglected previously. Knowledge of δ σ 2 ( ω ) allows to estimate value of the so-called unitary localization length as ξ u ≈ l exp ( 1.6 g 2 ) where Drude conductivity is given by σ 0 = ge 2 / h . This estimation underpins the statement of the linear growth of σ 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.