Universal scaling, beta function, and metal-insulator transitions

TL;DR

This paper reveals a universal scaling behavior of longitudinal resistance near metal-insulator transitions across various systems, supported by numerical and experimental data, highlighting a common beta function form and reflection symmetry.

Contribution

It introduces a universal scaling form and beta function for resistance in quantum critical regions, unifying diverse metal-insulator transition phenomena.

Findings

Universal resistance scaling form identified across different systems.

Reflection symmetry and logarithmic beta function observed over wide resistance ranges.

Implications for understanding two-dimensional metal-insulator transitions discussed.

Abstract

We demonstrate a universal scaling form of longitudinal resistance in the quantum critical region of metal-insulator transitions, based on numerical results of three-dimensional Anderson transitions (with and without magnetic field), two-dimensional quantum Hall plateau to insulator transition, as well as experimental data of the recently discovered two-dimensional metal-insulator transition. The associated reflection symmetry and a peculiar logarithmic form of the beta function exist over a wide range in which the resistance can change by more than one order of magnitude. Interesting implications for the two-dimensional metal-insulator transition are discussed.