Classical Properties of Low-Dimensional Conductors: Giant Capacitance and Non-Ohmic Potential Drop

Abstract

The 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 σ(x) rather than on the local value of it, inhomogeneities of σ(x) produce giant capacitances C(ω) that show frequency dependence at relatively low ω, and electrical fields develop in vast regions around the inhomogeneities of σ(x). A theory of these phenomena is presented for 2D conductors.