We present a comprehensive study of the non-centrosymmetric semimetal
LaRhGe3​. Our transport measurements reveal evidence for electron-hole
compensation at low temperatures, resulting in a large magnetoresistance of
3000% at 1.8 K and 14 T. The carrier concentration is on the order of
1021/cm3, higher than typical semimetals. We predict theoretically
the existence of almost movable Weyl nodal lines that are protected
by the tetragonal space group. We discover superconductivity for the first time
in this compound with a Tc​ of 0.39(1) K and Bc​(0) of
2.1(1) mT, with evidence from specific heat and transverse-field muon spin
relaxation (μSR). LaRhGe3​ is a weakly-coupled type-I
superconductor, and we find no evidence for time-reversal symmetry breaking in
our zero-field μSR. We study the electrical transport in the normal
state and find an unusual ∼T3 dependence at low temperature while
Seebeck coefficient and thermal conductivity measurements reveal a peak in the
same temperature range. We conclude that the transport properties of LaRhGe3​
in its normal state are strongly influenced by electron-phonon interactions.
Furthermore, we examine the temperature dependent Raman spectra of LaRhGe3​
and find that the lifetime of the lowest energy A1​ phonon is dominated by
phonon-electron scattering instead of anharmonic decay