Probing the superconducting gap structure of ScRuSi via $\mu \mathrm{SR}$ and first-principles calculations

In this study, we present a thorough investigation into the superconducting state of the ruthenium-based ternary equiatomic compound ScRuSi. Our analysis combines experimental techniques, including muon spin rotation/relaxation ($\mu \mathrm{SR}$) and low-temperature resistivity measurements, with theoretical insights derived from first-principles calculations. The low-temperature resistivity measurements reveal a distinct superconducting phase transition in the orthorhombic structure of ScRuSi at a critical temperature ($T_{\text{C}}$) of $2.5K$. Further, the TF-$\mu \mathrm{SR}$ analysis yields a gap-to-critical-temperature ratio of $2\Delta /k_B{T}_C=2.71$, a value consistent with results obtained from previous heat capacity measurements. The temperature dependence of the superconducting normalized depolarization rate is fully described by the isotropic $s$-wave gap model. Additionally, zero-field $\mu \mathrm{SR}$ measurements indicate that the relaxation rate remains nearly identical below and above $T_{\text{C}}$. This observation strongly suggests the preservation of time-reversal symmetry within the superconducting state. By employing the McMillan-Allen-Dynes equation, we calculate a $T_{\text{C}}$ of $2.11K$ from first-principles calculations within the density functional theory framework. This calculated value aligns closely with the experimentally determined critical temperature. The coupling between the low-frequency phonon modes and the transition metal d-orbital states play an important role in governing the superconducting pairing in ScRuSi. The combination of experimental and theoretical approaches provides a comprehensive microscopic understanding of the superconducting nature of ScRuSi, offering insights into its critical temperature, pairing symmetry, and the underlying electron-phonon coupling mechanism.