We study microscopic structures of monopole pair vibrational modes and associated two-neutron transfer amplitudes in neutron-rich Sn isotopes by means of the linear response formalism of the quasiparticle random phase approximation (QRPA). For this purpose we introduce a method to decompose the transfer amplitudes with respect to two-quasiparticle components of the QRPA eigenmode. It is found that pair-addition vibrational modes in neutron-rich Sn132-140 and the pair rotational modes in Sn142-150 are commonly characterized by coherent contribution of quasaiparticle states having high orbital angular momenta l greater than or similar to 5, which suggests transfer of a spatially correlated neutron pair. The calculation also predicts a high-lying pair vibration, the giant pair vibration, emerging near the one-neutron separation energy in Sn110-130, and we find that they have the same di-neutron characters as that of the low-lying pair vibration in Sn132-140.