We discuss the charge distributions across the bulk of a two-dimensional electron-gas system that is on an integer or fractional quantum Hall plateau. Our analysis is based on a relation, derived from the long-wavelength limit of the bulk density-density response function, between the induced charge and leading derivatives of a slowly varying Hall potential. We use the Wiener-Hopf method to solve the coupled response and Poisson equations. Unlike the integer case, treated in previous work, the induced charge in the fractional case can alternate in sign.

• Received 3 November 1997

DOI:https://doi.org/10.1103/PhysRevB.57.7119