Possible bound nuclei beyond the two-neutron drip line in the $50\leqslant Z \leqslant 70$ region.

The possible bound nuclei beyond the two-neutron drip line in the $50\leqslant Z \leqslant 70$ region are investigated by using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1. Bound nuclei beyond the drip line of $_{56}$Ba, $_{58}$Ce, $_{62}$Sm, $_{64}$Gd and $_{66}$Dy are predicted, forming peninsulas of stability in the nuclear landscape. Near these peninsulas, there are several multi-neutron emitters which are stable against two-neutron emission but unstable against multi-neutron emission. The underlying mechanism is investigated by studying the total energy, Fermi surface, quadrupole deformation and single-neutron spectrum in the canonical basis. It is found that the deformation effect is crucial for the peninsulas of stability, and pairing correlations are also essential in specific cases. The dependence on the deformation evolution for the stability against neutron emissions is discussed. %Taking Ba and Sm isotopes near the drip line as examples, the evolution of the canonical single-neutron spectra and pairing energies are discussed in detail to further understand the mechanism in a microscopic way.