  Two-neutron transfer associated with the pair correlation in superfluid
neutron-rich nuclei is studied with focus on low-lying $0^+$ states in Sn
isotopes beyond the N=82 magic number. We describe microscopically the
two-neutron addition and removal transitions by means of the
Skyrme-Hartree-Fock-Bogoliubov mean-field model and the continuum quasiparticle
random phase approximation formulated in the coordinate space representation.
It is found that the pair transfer strength for the transitions between the
ground states becomes significantly large for the isotopes with $A \ge 140$,
reflecting very small neutron separation energy and long tails of the weakly
bound $3p$ orbits. In $^{132-140}$Sn, a peculiar feature of the pair transfer
is seen in transitions to low-lying excited $0^+$ states. They can be regarded
as a novel kind of pair vibrational mode which is characterized by an
anomalously long tail of the transition density extending to far outside of the
nuclear surface, and a large strength comparable to that of the ground-state
transitions. The presence of the weakly bound neutron orbits plays a central
role for these anomalous behaviors.
