Barium-rhodium silicide $\mathrm{BaRh}{\mathrm{Si}}_2$ has been successfully synthesized using a high-pressure technique at 6 GPa. X-ray Rietveld analysis and scanning transmission electron microscopy studies revealed that $\mathrm{BaRh}{\mathrm{Si}}_2$ is isostructural to $\mathrm{BaIrS}{\mathrm{i}}_2$, within the noncentrosymmetric space group $C{222}_1$ with the lattice parameters $a=14.9777\left(1\right)\AA , b=8.0517\left(1\right)\AA$, and $c=8.0551\left(1\right)\AA$. Electrical resistivity, magnetic moment, and specific-heat measurements indicate that $\mathrm{BaRh}{\mathrm{Si}}_2$ is a type-II superconductor with a critical temperature $T_{\mathrm{c}}\sim 5.1\mathrm{K}$, an upper critical field $H_{\mathrm{c}2}\left(0\right)\sim 32$ kOe, and a Ginzburg-Landau parameter ${\kappa }_{\mathrm{GL}}\sim 56$. The superconductivity is a Bardeen-Cooper-Schrieffer (BCS)-like state with moderate electron-phonon coupling ${\lambda }_{\mathrm{ep}}\sim 0.6$ and weak electron correlation ${\lambda }_{\mathrm{ee}}\sim 0.1$. Phonon mediation seems to be dominant for the Cooper pairing. The ab initio calculations revealed that $\mathrm{BaRh}{\mathrm{Si}}_2$ has three pairs of Fermi surfaces split by spin-orbit coupling. The band splitting energy is around ${\mathrm{\Delta }}_{\mathrm{ASO}}\sim 0.03$ eV near $E_{\mathrm{F}}$, which is rather smaller than that ($\sim 0.07$ eV) in $\mathrm{BaIrS}{\mathrm{i}}_2$.

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• Critical field
• Superconductivity
• Noncentrosymmetric materials
• Density functional calculations
• Resistivity measurements
• Scanning transmission electron microscopy
• Specific heat measurements
• X-ray diffraction