Nodeless superconductivity in the noncentrosymmetric Mo${}_3$Rh${}_2$N superconductor: a $\mu$SR study

The noncentrosymmetric superconductor Mo${}_3$Rh${}_2$N, with $T_c=4.6$ K, adopts a $\beta$-Mn-type structure (space group $P$4${}_1$32), similar to that of Mo${}_3$Al${}_2$C. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation ($\mu$SR). The low-temperature superfluid density, measured via transverse-field (TF)-$\mu$SR, evidences a fully-gapped superconducting state with $\Delta_0 = 1.73 k_$\mathrm{B}$T_c$,verycloseto1.76$k_$\mathrm{B}$T_c$ - the BCS gap value for the weak coupling case, and a magnetic penetration depth ${\lambda }_0=586$ nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-$\mu$SR measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF-and ZF-$\mu$SR results evidence a spin-singlet pairing in Mo${}_3$Rh${}_2$N.