Effective Drag Between Strongly Inhomogeneous Layers: Exact Results and Applications

TL;DR

This paper derives an exact formula for the effective transresistance in inhomogeneous layered systems, analyzing its behavior near the metal-insulator transition and revealing how correlations influence its evolution.

Contribution

It generalizes Dykhne's method to include frictional drag between layers, providing exact results for inhomogeneous 2D systems near the MIT.

Findings

Effective transresistance behavior depends on component correlations.

In electron layers, transresistance can be monotonic or have a maximum.

In electron-hole layers, transresistance is negative with a minimum at the MIT.

Abstract

We generalize Dykhne's calculation of the effective resistance of a 2D two-component medium to the case of frictional drag between the two parallel two-component layers. The resulting exact expression for the effective transresistance, $\rho^D_{eff}$, is analyzed in the limits when the resistances and transresistances of the constituting components are strongly different - situation generic for the vicinity of the {\em classical} (percolative) metal-insulator transition (MIT). On the basis of this analysis we conclude that the evolution of $\rho^D_{eff}$ across the MIT is determined by the type of correlation between the components, constituting the 2D layers. Depending on this correlation, in the case of two electron layers, $\rho^D_{eff}$ changes either monotonically or exhibits a sharp maximum. For electron-hole layers $\rho^D_{eff}$ is negative and $|\rho^D_{eff}|$ exhibits a sharp minimum at the MIT.