On the Possibility of Experimental Verification of the Some Localization Theory Predictions

TL;DR

This paper explores how the nonlinear voltage-distance relationship in transport equations can be experimentally used to probe the spatial non-locality of diffusion in disordered systems, providing insights into electron wave function properties near localization thresholds.

Contribution

It proposes a method to experimentally verify localization theory predictions by analyzing the nonlinear dependence of voltage on sample size and dispersion scale.

Findings

Voltage drop depends nonlinearly on sample size and dispersion scale.

Potential to determine the multifractal dimension of electron wave functions.

Experimental approach to study Anderson localization effects.

Abstract

The spatial non-locality (dispersion) of the transport equations results in a nonlinear dependence of the voltage drop $U$ on the distance between the points of measuring. Therefore the results of the usual two-probe measurements of the conductivity depend essentially on the relation between the sample linear size $L$ and the spatial dispersion scale $R$ of the generalized diffusion coefficient $D(q,\omega)$. This makes it possible to get information on the character of the spatial non-locality of $D(q,\omega)$ in the Anderson localization regime and, in particular, on the correlation multifractal dimension $D_{2}$ of the electron wave functions near the mobility edge.