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We have investigated the superconducting properties of the noncentrosymmetricsuperconductor 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 diffractionstudy. Magnetic susceptibility, electrical resistivity and specific heat datareveal 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 groundstate 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 fieldstrongly indicate a type-I behaviour. Type-I superconductivity in this compoundis also inferred from the Ginzburg-Landau parameter, $\kappa$ = 0.25. Varioussuperconducting parameters, including the electron-phonon coupling strength,penetration depth and coherence length, characterize LaRhSi$_{3}$ as a moderatedirty-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 $\pm$ 0.1mT, which is in very good agreement with that estimated from the transversefield $\mu$SR measurement that gives $H_{c0}$ = 17.2 $\pm$ 0.1 mT. Thetransverse field $\mu$SR results are consistent with conventional type-Isuperconductivity in this compound. Further, the zero-field $\mu$SR resultsindicate that time reversal symmetry is preserved when entering thesuperconducting state, also supporting a singlet pairing superconducting groundstate in LaRhSi$_{3}$.

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