We predict the existence of a Dirac state in a monolayer ${\mathrm{TiB}}_2$ sheet $\left(m\text{−}{\mathrm{TiB}}_2\right)$, a two-dimensional metal diboride, based on first-principles calculations. The band structure of $m\text{−}{\mathrm{TiB}}_2$ is found to be characterized with anisotropic Dirac cones with the largest Fermi velocity of $0.57\times {10}^6$ m/s, which is about one-half of that of graphene. The Dirac point is located at the Fermi level between the $K$ and $\Gamma$ points, with the Dirac states arising primarily from the $d$ orbitals of Ti. Freestanding $m\text{−}{\mathrm{TiB}}_2$ exhibits a bending instability, so that a planar $m\text{−}{\mathrm{TiB}}_2$ needs to be stabilized on a substrate. The calculation of $m\text{−}{\mathrm{TiB}}_2$ on a $h$-BN substrate reveals a negligible influence of the $h$-BN substrate on the electronic properties of $m\text{−}{\mathrm{TiB}}_2$. Our findings extend the Dirac materials to metal diborides.

• Received 22 August 2014
• Revised 19 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.161402