Multiple robust Dirac states in hexagonal lattice induced by p-d electron-counting rule and bilayer stacking

In this paper, we predict two-dimensional transition metal boride TiB2C2 and HfB2C2 nanosheets, which exhibit favorable mechanical and thermal properties. Young's moduli of TiB2C2 and HfB2C2 are 137.8 and 128.9 N/m, respectively. Both nanosheets could sustain up to 500 K based on our ab initio molecular dynamics results. In addition, both nanosheets are semimetallic, exhibiting 12 Dirac cones in the first Brillouin zone, six pairs of which form compensated electron-hole pockets. Under different types of external strains, both TiB2C2 and HfB2C2 are robust, and the Dirac cones could be tuned to be anisotropic. We propose that the multiple Dirac cones are induced by a combination of the p-d electron-counting rule and bilayer stacking; to verify our opinion, we also predicted and proved that TB2Si2 (T = Ti, Zr, Hf) are mechanical stable two-dimensional nanosheets with multiple Dirac cones based on phonon and electronic band structure calculations.