Universal scaling in disordered systems and nonuniversal exponents

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 perovskitesranging 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, x associated with the scaling was found to be nonuniversal and exhibits structure. For two-dimensional (2D) weakly localized systems, the nonlinearity exponent x is 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 (x ≈ 0.08 n). This poses a serious theoretical challenge. Various results are compared with predictions of the existing theories.

Effect of rapid thermal annealing on barrier height and 1/f noise of Ni/GaN Schottky barrier diodes

“…It is well known that I-V-T measurements give valuable information about conduction mechanisms in various systems. 25,[35][36][37][38] Therefore, I-V-T measurements are performed for D0 and D450/60 s in the temperature range of 80-320 K, as shown in Figs. 2(a) and 2(b), respectively.…”

Effect of Annealing Temperature on the Structural and the Electrical Transport Properties of La2NiMnO6 Nanoparticles

“…The value of was found to be . It should be mentioned here that this value of satisfies the unique phenomenal relation established experimentally by Bardhan et al in studying non‐Ohmic electrical conduction in various disordered systems. Here n is a natural integer.…”

“…Figure (b) shows the master curve of data by the data collapse method . The existence of voltage scale is clearly visible from the excellent data collapse up to .…”

“…Figure (b) shows the result of merging data of Figure (a) into a master curve by the data collapse method . Following this method, the conductance of the LNMO700 sample was divided by its Ohmic value and the voltage was kept unaltered that is the onset voltage was considered to be 1.…”

Gap states controlled transmission through 1D Metal-Nanotube junction

“…In the first method a crossover point V o is chosen at which the conductance deviates significantly from the zero field conductance G o by some arbitrary fraction ǫ, such that the conductance G = G o (1 + ǫ). In the second method [15,16] based on the existence of a single voltage scale V o , a set of I−V curves can be characterized by a number x, called the nonlinearity exponent. In this scaling approach, the conductance G(M, V ) is given by the scaling relation:…”