On the issue of universality of critical exponents in the quantum Hall effect mode

Abstract

A critical analysis of the work performed within the framework of the two-parameter scaling concept is carried out, and a brief review of modern percolation models for the quantum plateau–plateau phase transition in the quantum Hall effect mode is presented. The work was motivated by a discussion of theoretical models for describing the effect of overlapping and mixing the densities of localized and delocalized states at Landau levels on the universality of critical exponents.

Three-dimensional quasiquantized Hall insulator phase in SrSi2

“…The isotherms of ρ xx for such magnetic field induced metal-insulator transitions typically scale with λ l and thus obey a universal scaling law with the parameter (B-B c )T −1/ζ . This applies to transitions between the QHL and QHI in 2D systems [35] as well as to transitions between the 3D QQHL and the ordinary HI [38,40], as in ZrTe 5 [19]. In Fig.…”

“…Conversely, if ρ xx decreases with decreasing T , the state is regarded as a metal. In a 2D electron system, the transition between an insulating phase and a metallic phase in the quantum Hall regime can be characterized by a critical magnetic-field value B c , for which ρ xx is T independent and where the derivative of the T dependence changes sign on each side of the transition [35]. In experiments, B c is usually extracted from the intersection of ρ xx (B) curves measured at various values of T [1].…”