Tetrahedral shape of ${}^{110}$Zr from covariant density functional theory in 3D lattice space

Covariant density functional theory is solved in 3D lattice space by implementing the preconditioned conjugate gradient method with a filtering function (PCG-F). It considerably improves the computational efficiency compared to the previous inverse Hamiltonian method (IHM). This new method is then applied to explore the tetrahedral shape of ${}^{110}$Zr in the full deformation space. The ground state of ${}^{110}$Zr is found to have a tetrahedral shape, but the deformations ${\beta }_{31}$ and ${\beta }_{33}$ greatly soften the potential energy surface. This effect is analysed with the microscopic evolution of the single-particle levels near the Fermi surface driven by the deformation.