Ratchet effects for vortices in superconductors with periodic pinning arrays

Using numerical simulations we show that novel transport phenomena can occur for vortices moving in periodic pinning arrays when two external perpendicular ac drives are applied. In particular, we find a ratchet effect where the vortices can have a net dc drift even in the absence of a dc drive. This ratchet effect can occur for ac drives which create orbits that break one or more reflection symmetries.