  We examine a charge lattice coupled to a one-dimensional asymmetric potential
in the presence of an applied magnetic field, which induces gyrotropic effects
in the charge motion. This system could be realized for Wigner crystals in
nanostructured samples, dusty plasmas, or other classical charge-ordered states
where gyrotropic motion and damping can arise. For zero magnetic field, an
applied external ac drive can produce a ratchet effect in which the particles
move along the easy flow direction of the substrate asymmetry. The zero field
ratchet effect can only occur when the ac drive is aligned with the substrate
asymmetry direction; however, when a magnetic field is added, the gyrotropic
forces generate a Hall effect that leads to a variety of new behaviors,
including a transverse ratchet motion that occurs when the ac drive is
perpendicular to the substrate asymmetry direction. We show that this system
exhibits commensuration effects as well as reversals in the ratchet effect and
the Hall angle of the motion. The magnetic field also produces a nonmonotonic
ratchet efficiency when the particles become localized at high fields.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Statistical Mechanics