  The tunneling of the massless Dirac fermions through a vector potential
barrier are theoretically investigated, where the vector potential can be
introduced by the very high and very thin (delta-function) magnetic potential
barriers. We show that, distinct from the previously studied electric barrier
tunneling, the vector potential barriers are more transparent for
pseudospin-1/2 Dirac fermions but more obstructive for pseudospin-1 Dirac
fermions. By tuning the height of the vector potential barrier, the
pseudospin-1/2 Dirac fermions remain transmitted, whereas the transmission of
the pseudospin-1 Dirac fermions is forbidden, leading to a pseudospin filtering
effect for massless Dirac fermions.
