Universal scaling in disordered systems and non-universal exponents

TL;DR

This paper explores universal and non-universal scaling behaviors in disordered systems' conduction under electric fields, revealing diverse exponents and transitions that challenge existing theories across different dimensions and localization regimes.

Contribution

It introduces a one-parameter scaling framework for disordered systems, uncovers non-universal exponents, and identifies a temperature-induced transition in 2D systems, challenging current theoretical models.

Findings

Non-universality of the nonlinearity exponent  x in various systems.

Quantized exponent  x  0.08 n in 3D strongly localized systems.

Temperature-induced scaling-nonscaling transition (SNST) in 2D strongly localized systems.

Abstract

The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites, composites, metallic alloys, double perovskites - ranging from strongly localized systems to weakly localized ones, from strongly correlated ones to weakly correlated ones. Theories have singularly failed to predict any universal trend resulting in separate theories for separate systems. Here we discuss an one-parameter scaling that has recently been found to give a systematic account of the field-dependent conductance in two diverse, strongly localized systems of conducting polymers and manganites. The nonlinearity exponent, \textit{x} associated with the scaling was found to be nonuniversal and exhibits structure. For two-dimensional (2D) weakly localized systems, the nonlinearity exponent \textbf{\textit{x}} is $\geqslant 7$ and is roughly inversely proportional to the sheet resistance. Existing theories of weak localization prove to be adequate and a complete scaling function is derived. In a 2D strongly localized system a temperature-induced scaling-nonscaling transition (SNST) is revealed. For three-dimensional (3D) strongly localized systems the exponent lies between -1 and 1, and surprisingly is quantized (\textit{x} $\approx$ 0.08 \textit{n}). This poses a serious theoretical challenge. Various results are compared with predictions of the existing theories.