  Theoretical evidence of the existence of 12 inequivalent Dirac cones at the
vicinity of the Fermi energy in monolayered ZrB$_2$ is presented.
Two-dimensional ZrB$_2$ is a mechanically stable d- and p-orbital compound
exhibiting a unique electronic structure with two Dirac cones out of
high-symmetry points in the irreducible Brillouin zone with a small
electron-pocket compensation. First-principles calculations demonstrate that
while one of the cones is insensitive to lattice expansion, the second cone
vanishes for small perturbation of the vertical Zr position. Internal symmetry
breaking with external physical stimuli, along with the relativistic effect of
SOC, is able to remove selectively the Dirac cones. A rational explanation in
terms of d- and p-orbital mixing is provided to elucidate the origin of the
infrequent amount of Dirac cones in a flat structure. The versatility of
transition metal d-orbitals combined with the honeycomb lattice provided by the
B atoms yields novel features never observed in a two-dimensional material.
