Interplay between p − and d − orbitals yields multiple Dirac states in one- and two-dimensional CrB ₄

Abstract Theoretical evidence of the existence of six inequivalent and six threefold degenerate pairs of Dirac cones in the low-spectrum diagram of monolayered hexagonal CrB ₄ is provided. The four d electrons of the Cr atom 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 additional 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, CrB ₄ is a semimetal with compensated electron–hole pockets. As the 2D layer is shaped into finite-width ribbons, one actual and one symmetry-frustrated Dirac point are observed at the Fermi level, yielding massless fermions in a 1D nano-structure with no topological insulating features. A rational explanation in terms of periodic boundary conditions across the ribbon axis is given to unveil the origin of the Dirac point.