Nonlinearity exponents in disordered systems    [PDF]

K. K. Bardhan, D. Talukdar
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 a recent one-parameter scaling that has been found to give a systematic account of the field-dependent conductance in two strongly localized systems of conducting polymers and manganites. The nonlinearity exponent, \textit{x} associated with the scaling was unexpectedly found to possess multiple values. We find that the scaling applies to all other systems as mentioned. For 3D strongly localized systems the exponent lies between -1 and 1, and surprisingly, is quantized (\textit{x} $\approx$ 0.08 \textit{n}). For 2D weakly localized systems, the nonlinearity exponent \textbf{\textit{x}} is $\geqslant 9$ and is roughly inversely proportional to the sheet resistance. Existing theories of weak localization prove to be adequate in explaining the proposed scaling which however poses a challenge for theories in case of strong localization.
View original: http://arxiv.org/abs/1305.0031