Background: The study of exotic nuclei far from the $\beta$ stability line is stimulated by the development of radioactive ion beam facilities worldwide and brings opportunities and challenges to existing nuclear theories. Including self-consistently the nuclear superfluidity, deformation, and continuum effects, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has turned out to be successful in describing both stable and exotic nuclei. Due to several challenges, however, the DRHBc theory has only been applied to study light nuclei so far.

The predictive power of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for nuclear mass is examined in the superheavy region, $102\le Z\le 120$. The accuracy of predicting the 10 (56) measured (measured and empirical) masses is 0.635 (0.642) MeV, in comparison with 0.515 (1.360) MeV by WS4 and 0.910 (2.831) MeV by FRDM. Possible stability against multineutron emission beyond the two-neutron drip line is explored by the DRHBc theory, which takes into account simultaneously the deformation effects, the pairing correlations, and the continuum effects. Nuclei stable against two- and multineutron emissions beyond the two-neutron drip line are predicted in ${}_{106}\mathrm{Sg}, {}_{108}\mathrm{Hs}, {}_{110}\mathrm{Ds}$, and ${}_{112}\mathrm{Cn}$ isotopic chains, forming a peninsula of stability adjacent to the nuclear mainland. This stability is mainly due to the deformation which significantly affects the shell structure around the Fermi surface. The pairing correlations and continuum influence the stability peninsula in a self-consistent way.

Halos and changes of nuclear magicities have been extensively investigated in exotic nuclei during past decades. The newly discovered ${}^{39}\mathrm{Na}$ with the neutron number $N=28$ provides a new platform to explore such novel phenomena near the neutron dripline of the sodium isotopic chain. We study the shell property and the possible halo structure in ${}^{39}\mathrm{Na}$ within the deformed relativistic Hartree-Bogoliubov theory in continuum. It is found that the lowering of $2p$ orbitals in the spherical limit results in the collapse of the $N=28$ shell closure in ${}^{39}\mathrm{Na}$, and a well-deformed ground state is established. The pairing correlations and the mixing of $pf$ components driven by deformation lead to the occupation of weakly bound or continuum $p$-wave neutron orbitals. An oblate halo is therefore formed around the prolate core in ${}^{39,41}\mathrm{Na}$, making ${}^{39}\mathrm{Na}$ a single nucleus with the coexistence of several exotic structures, including the quenched $N=28$ shell closure, Borromean structure, deformed halo, and shape decoupling. The microscopic mechanisms behind the shape decoupling phenomenon and the development of halos towards dripline are revealed.

Particles in the classically forbidden regions are studied based on the deformed relativistic Hartree-Bogoliubov theory in continuum with PC-PK1 for magnesium isotopes. By analyzing the neutron and proton radii, it is found that the largest deviations from the empirical values appear at the predicted neutron halo nuclei ${}^{42}\mathrm{Mg}$ and ${}^{44}\mathrm{Mg}$. Consistently, notable increases at ${}^{42}\mathrm{Mg}$ and ${}^{44}\mathrm{Mg}$ are found in the total number of neutrons in the classically forbidden regions, which includes the number of neutrons in continuum. It is shown that the deformation effect, in general, increases the number of particles in the classically forbidden regions below the continuum threshold. The most deeply bound single-particle states play the dominant roles in the increase caused by deformation.

Possible bound nuclei beyond the two-neutron drip line in the $50\le Z\le 70$ region are investigated by using the deformed relativistic Hartree-Bogoliubov theory in continuum with density functional PC-PK1. Bound nuclei beyond the drip lines of ${}_{56}\mathrm{Ba}$, ${}_{58}\mathrm{Ce}$, ${}_{62}\mathrm{Sm}$, ${}_{64}\mathrm{Gd}$, and ${}_{66}\mathrm{Dy}$ are predicted, forming peninsulas of stability in the nuclear landscape. Near these peninsulas, several multineutron emitters are predicted. The underlying mechanism of the peninsulas of stability is investigated by studying the total energy, Fermi surface, quadrupole deformation, and the single-neutron spectrum in the canonical basis. It is found that the deformation effect is crucial for forming the peninsulas of stability, and pairing correlations are also essential in specific cases. The dependence on the deformation evolution is also discussed. The decay rates of multineutron radioactivity in Ba and Sm isotopic chains are estimated by using the direct decay model.