  Motivated by the recently discovered microwave-induced ``zero-resistance''
states in two-dimensional electron systems, we study the microwave
photoconductivity of a two-dimensional electron gas (2DEG) subject to a
unidirectional static periodic potential. The combination of this potential,
the classically strong magnetic field, and the microwave radiation may result
in an anisotropic negative conductivity of the 2DEG. Similar to the case of a
smooth random potential, two mechanisms contribute to the negative
photoconductivity. The displacement mechanism arises from electron transitions
due to disorder-assisted microwave absorption and emission. The
distribution-function mechanism arises from microwave-induced changes in the
electron distribution. However, the replacement of a smooth random potential by
the unidirectional one, leads to different relative strengths of the two
contributions to the photoconductivity. The distribution function mechanism
dominates the photoconductivity in the direction of the static potential
modulation, while both mechanisms contribute equally strongly to the
photoconductivity in the perpendicular direction. The unidirectionality of the
static potential simplifies greatly the evaluation of the photoconductivities,
which follow directly from Fermi's golden rule.
