Specific heat and $\mu$SR study on the noncentrosymmetric superconductor LaRhSi3

We have investigated the superconducting properties of the noncentrosymmetric superconductor LaRhSi$_{3}$ by performing magnetization, specific heat, electrical resistivity and muon spin relaxation ($\mu$SR) measurements. LaRhSi$_{3}$ crystallizes with the BaNiSn$_{3}$-type tetragonal structure (space group \textit{I4 mm}) as confirmed through our neutron diffraction study. Magnetic susceptibility, electrical resistivity and specific heat data reveal a sharp and well defined superconducting transition at $T_{c}$ = 2.16 $\pm$ 0.08 K. The low temperature specific heat data reveal that LaRhSi$_{3}$ is a weakly coupled bulk BCS superconductor and has an s-wave singlet ground state with an isotropic energy gap of $\sim$ 0.3 meV, $2 \Delta_{0} /k_{B}T_{c}$ = 3.24. The specific heat data measured in applied magnetic field strongly indicate a type-I behaviour. Type-I superconductivity in this compound is also inferred from the Ginzburg-Landau parameter, $\kappa$ = 0.25. Various superconducting parameters, including the electron-phonon coupling strength, penetration depth and coherence length, characterize LaRhSi$_{3}$ as a moderate dirty-limit superconductor. A detailed study of the magnetic field-temperature ($H-T$) phase diagram is presented and from a consideration of the free energy, the thermodynamic critical field, $H_{c0}$ is estimated to be 17.1 $\pm$ 0.1 mT, which is in very good agreement with that estimated from the transverse field $\mu$SR measurement that gives $H_{c0}$ = 17.2 $\pm$ 0.1 mT. The transverse field $\mu$SR results are consistent with conventional type-I superconductivity in this compound. Further, the zero-field $\mu$SR results indicate that time reversal symmetry is preserved when entering the superconducting state, also supporting a singlet pairing superconducting ground state in LaRhSi$_{3}$.