Hall current and electron polarizability of a two-dimensional electron gas subjected to weak superlattice potentials

A theory of the Hall effect in two-dimensional electron systems subjected to weak periodic modulation of the background potential is presented. It is shown that the nondissipative Hall current is strongly affected by the static electron polarizability, which is responsible for the nonmonotonic sequence of quantum Hall plateaus in the dependence on the magnetic field strength. This static electron polarizability is quantized whenever the Fermi energy lies within an energy gap.