Prediction of a Dirac state in monolayer<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">TiB</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

We predict the existence of a Dirac state in a monolayer ${\mathrm{TiB}}_{2}$ sheet $(m\text{\ensuremath{-}}{\mathrm{TiB}}_{2})$, a two-dimensional metal diboride, based on first-principles calculations. The band structure of $m\text{\ensuremath{-}}{\mathrm{TiB}}_{2}$ is found to be characterized with anisotropic Dirac cones with the largest Fermi velocity of $0.57\ifmmode\times\else\texttimes\fi{}{10}^{6}$ m/s, which is about one-half of that of graphene. The Dirac point is located at the Fermi level between the $K$ and $\ensuremath{\Gamma}$ points, with the Dirac states arising primarily from the $d$ orbitals of Ti. Freestanding $m\text{\ensuremath{-}}{\mathrm{TiB}}_{2}$ exhibits a bending instability, so that a planar $m\text{\ensuremath{-}}{\mathrm{TiB}}_{2}$ needs to be stabilized on a substrate. The calculation of $m\text{\ensuremath{-}}{\mathrm{TiB}}_{2}$ on a $h$-BN substrate reveals a negligible influence of the $h$-BN substrate on the electronic properties of $m\text{\ensuremath{-}}{\mathrm{TiB}}_{2}$. Our findings extend the Dirac materials to metal diborides.

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