  We consider magnetotransport in a disordered two-dimensional electron gas in
the presence of a periodic modulation in one direction. Existing quasiclassical
and quantum approaches to this problem account for Weiss oscillations in the
resistivity tensor at moderate magnetic fields, as well as a strong
modulation-induced modification of the Shubnikov-de Haas oscillations at higher
magnetic fields. They do not account, however, for the operation at even higher
magnetic fields of the integer quantum Hall effect, for which quantum
interference processes are responsible. We then introduce a field-theory
approach, based on a nonlinear sigma model, which encompasses naturally both
the quasiclassical and quantum-mechanical approaches, as well as providing a
consistent means of extending them to include quantum interference corrections.
A perturbative renormalization-group analysis of the field theory shows how
weak localization corrections to the conductivity tensor may be described by a
modification of the usual one-parameter scaling, such as to accommodate the
anisotropy of the bare conductivity tensor. We also show how the two-parameter
scaling, conjectured as a model for the quantum Hall effect in unmodulated
systems, may be generalized similarly for the modulated system. Within this
model we illustrate the operation of the quantum Hall effect in modulated
systems for parameters that are realistic for current experiments.
