Exploring Superconductivity in Ba$_{3}$Ir$_{4}$Ge$_{16}$: Experimental and Theoretical Insights

We explore both experimental and theoretical aspects of the superconducting properties in the distinctive layered caged compound, Ba$_{3}$Ir$_{4}$Ge$_{16}$. Our approach integrates muon spin rotation and relaxation ($\mu$SR) measurements with magnetization and heat capacity experiments, accompanied by first-principle calculations. The compound's bulk superconductivity is unequivocally established through DC magnetization measurements, revealing a critical temperature ($T_\mathrm{C}$) of 5.7 K. A noteworthy characteristic observed in the low-temperature superfluid density is its saturating behavior, aligning with the features typical of conventional Bardeen-Cooper-Schrieffer (BCS) superconductors. The assessment of moderate electron-phonon coupling superconductivity is conducted through transverse field $\mu$SR measurements, yielding a superconducting gap to $T_\mathrm{C}$ ratio ($2\Delta(0)/k_\mathrm{B}T_\mathrm{C}$) of 4.04, a value corroborated by heat capacity measurements. Crucially, zero field $\mu$SR measurements dismiss the possibility of any spontaneous magnetic field emergence below $T_\mathrm{C}$, highlighting the preservation of time-reversal symmetry. Our experimental results are reinforced by first-principles density functional calculations, underscoring the intricate interplay between crystal structure and superconducting order parameter symmetry in polyhedral caged compounds. This comprehensive investigation enhances our understanding of the nuanced relationship between crystal structure and superconductivity in such unique compounds.