Classical properties of low-dimensional conductors: Giant capacitance and non-Ohmic potential drop

TL;DR

This paper explores unique electrical properties of low-dimensional conductors, revealing how inhomogeneities lead to giant, frequency-dependent capacitances and extensive electric fields, differing fundamentally from 3D conductors.

Contribution

It presents a theoretical framework for understanding giant capacitance and non-Ohmic potential drops in 2D conductors caused by inhomogeneities.

Findings

Inhomogeneities produce giant, frequency-dependent capacitances.

Electric fields extend over large regions around inhomogeneities.

The theory explains non-Ohmic potential drops in 2D conductors.

Abstract

Electrical field arising around an inhomogeneous conductor when an electrical current passes through it is not screened, as distinct from 3D conductors, in low-dimensional conductors. As a result, the electrical field depends on the global distribution of the conductivity sigma(x) rather than on the local value of it, inhomogeneities of sigma(x) produce giant capacitances C(omega) that show frequency dependence at relatively low omega, and electrical fields develop in vast regions around the inhomogeneities of sigma(x). A theory of these phenomena is presented for 2D conductors.