Prediction of $\mathrm{TiRhAs}$ as a Dirac Nodal Line Semimetal via First-Principles Calculations

Using first-principles calculations, we predict that $\mathrm{TiRhAs}$, a previously synthesized compound, is a Dirac nodal line (DNL) semimetal. The DNL in this compound is found to be protected both by the combination of inversion and time-reversal symmetry, and by a reflection symmetry, in the absence of spin-orbit coupling (SOC). Our calculations show that band velocities associated with the nodal line have a high degree of directional anisotropy, with in-plane velocities ${v}_{\ensuremath{\perp}}$ perpendicular to the nodal line between $1.2--2.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ m/s. The crossings along the DNL are further found to exhibit a prominent and position-dependent tilt along directions perpendicular to the nodal line. We calculate ${\mathbb{Z}}_{2}$ indices based on parity eigenvalues at time-reversal invariant momenta and show that $\mathrm{TiRhAs}$ is topological. A tight-binding model fit from our first-principles calculations demonstrates the existence of two-dimensional drumhead surface states on the surface Brillouin zone. Based on the small gapping of the DNL upon inclusion of SOC and the clean Fermi surface free from trivial bands, $\mathrm{TiRhAs}$ is a promising candidate for further studies of the properties of topological semimetals.