Conventional type-II superconductivity in locally non-centrosymmetric LaRh$_2$As$_2$ single crystals

We report on the observation of superconductivity in LaRh$_2$As$_2$, which is the analogue without $f$-electrons of the heavy-fermion system with two superconducting phases CeRh$_2$As$_2$. A zero-resistivity transition, a specific-heat jump and a drop in magnetic ac susceptibility consistently point to a superconducting transition at a transition temperature of $T_c = 0.28$\,K. The magnetic field-temperature superconducting phase diagrams determined from field-dependent ac-susceptibility measurements reveal small upper critical fields $\mu_{\mathrm{0}}H_{c2} \approx 12$\,mT for $H\parallel ab$ and $\mu_{\mathrm{0}}H_{c2} \approx 9$\,mT for $H\parallel c$. The observed $H_{c2}$ is larger than the estimated thermodynamic critical field $H_c$ derived from the heat-capacity data, suggesting that LaRh$_2$A$s_2$ is a type-II superconductor with Ginzburg-Landau parameters $\kappa^{ab}_{GL} \approx 1.9$ and $\kappa^{c}_{GL}\approx 2.7$. The microscopic Eliashberg theory indicates superconductivity to be in the weak-coupling regime with an electron-phonon coupling constant $\lambda_{e-ph} \approx 0.4$. Despite a similar $T_c$ and the same crystal structure as the Ce compound, LaRh$_2$As$_2$ displays conventional superconductivity, corroborating the substantial role of the 4$f$ electrons for the extraordinary superconducting state in CeRh$_2$As$_2$.