R Ru B 2 ( R = Y , Lu ) , topological superconductor candidates with hourglass-type Dirac ring

Topological properties and topological superconductivity in real materials have attracted intensive experimental and theoretical attention recently. Based on symmetry analysis and first-principles electronic structure calculations, we predict that $R\mathrm{Ru}{\mathrm{B}}_{2}$ $(R=\mathrm{Y}, \mathrm{Lu})$ are not only topological superconductor (TSC) candidates but also own the hybrid hourglass-type Dirac ring which is protected by the nonsymmorphic space group symmetry. Due to the band inversion around the time-reversal invariant $\mathrm{\ensuremath{\Gamma}}$ point in the Brillouin zone, $R\mathrm{Ru}{\mathrm{B}}_{2}$ also have Dirac topological surface states (TSSs). More importantly, their TSSs on the (010) surface are within the band gap of bulk and cross the Fermi level, which form single Fermi surfaces. Considering the fact that both $\mathrm{Y}\mathrm{Ru}{\mathrm{B}}_{2}$ and $\mathrm{Lu}\mathrm{Ru}{\mathrm{B}}_{2}$ are superconductors with respective superconducting transition temperatures $({T}_{c})$ of 7.6 K and 10.2 K, the superconducting bulks will likely induce superconductivity in the TSSs via the proximity effect. The ternary borides $R\mathrm{Ru}{\mathrm{B}}_{2}$ may thus provide a very promising platform for studying the properties of topological superconductivity and hourglass fermions in future experiments.