A triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc) has been developed to incorporate triaxial deformation, pairing correlations, and continuum effects in a fully microscopic and self-consistent way, aiming for a reliable description of triaxial exotic nuclei with extreme neutron-to-proton ratios. The TRHBc formalism is presented in detail, and its numerical implementation is benchmarked against the results from the axially deformed relativistic Hartree-Bogoliubov theory in continuum and the TRHB theory in harmonic-oscillator expansion. The TRHBc theory is applied to investigate the aluminum isotopes systematically, and the available data are well reproduced for the binding energies, one- and two-neutron separation energies, and charge radii. The nuclei near the one-neutron drip line, ${}^{40}\mathrm{Al}$ and ${}^{42}\mathrm{Al}$, are found to be triaxially deformed with one-neutron separation energies below 1 MeV. Possible neutron halos in the triaxial nuclei ${}^{40}\mathrm{Al}$ and ${}^{42}\mathrm{Al}$ are explored by examining the single-particle levels around the Fermi surface, including their composition and contribution to the total neutron density. The existence of neutron halos in ${}^{40}\mathrm{Al}$ and ${}^{42}\mathrm{Al}$ is also supported by the halo scale, which is comparable to other halo nuclei well-established previously. More importantly, the mechanism for the halo formation in ${}^{40}\mathrm{Al}$ is revealed to be the triaxial deformation, which results in the decoupling of the halo orbitals from those of the core.

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• Binding energy & masses
• Nuclear density functional theory
• Nuclear many-body theory
• Nuclear radii
• Nuclear structure & decays
• Nucleon distribution
• 20 ≤ A ≤ 38
• 39 ≤ A ≤ 58