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 $\sigma (x)$ 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.

• Received 16 April 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.096803