Multiple Dirac nodes and symmetry protected Dirac nodal line in orthorhombic α -RhSi

Exotic multifold topological excitations have been predicted and were recently observed in transition metal silicides like $\ensuremath{\beta}$-RhSi. Herein, we report that interesting topological features of RhSi are also observed in its orthorhombic $\ensuremath{\alpha}$ phase, which displays multiple types of Dirac nodes very close to the Fermi level ${\ensuremath{\varepsilon}}_{F}$. We discuss the symmetry analysis, band connectivity along high-symmetry lines using group representations, band structure, the nature of the Dirac points and of a nodal line occurring near ${\ensuremath{\varepsilon}}_{F}$ which is protected by the crystalline symmetry. The de Haas--van Alphen effect indicates a Fermi surface in agreement with the calculations. We find an elliptically shaped nodal line very close to ${\ensuremath{\varepsilon}}_{F}$ around and near the $S$ point on the ${k}_{y}\text{\ensuremath{-}}{k}_{z}$ plane that results from the intersection of two upside-down Dirac cones. Both Dirac points of the participating Kramers degenerate bands are only 5 meV apart; hence, an accessible magnetic field might induce a crossing between the spin-up partner of the upper Dirac cone and the spin-down partner of the lower Dirac cone, possibly explaining the anomalies observed in the magnetic torque. $\ensuremath{\alpha}$-RhSi is a unique system since all bands crossing ${\ensuremath{\varepsilon}}_{F}$ emerge from Dirac nodes.