Interplay between p- and d- orbitals yields multiple Dirac states in two-dimensional ZrB2 and CrB4

Theoretical evidence of the existence of 12 Dirac cones in the low-spectrum diagram of transition metal-rich monolayered hexagonal networks is provided. Both Zr and Cr are efficient in creating six additional cones with respect to graphene when combined with boron honeycomb lattices. The four d-electrons of Cr, and similarly the two d-electrons of Zr, are yielded to the B sublattices creating an isoelectronic structure to graphene where the interplay between p- and d-orbitals leads to the appearance of Dirac states on both one- and two-dimensional geometries. Ab initio calculations show that, although spin–orbit interaction splits the cone-shaped valence and conduction bands, monolayered ZrB2 and CrB4 are semimetals with compensated electron–hole pockets.