Discovery of Superconductivity and Electron-Phonon Drag in the Non-Centrosymmetric Weyl Semimetal LaRhGe$_3$

We present an exploration of the effect of electron-phonon coupling and broken inversion symmetry on the electronic and thermal properties of the semimetal LaRhGe$_3$. 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 $10^{21}\rm{/cm}^3$ with high carrier mobilities of $2000~\rm{cm}^2/\rm{Vs}$. When coupled to our theoretical demonstration of symmetry-protected $\textit{almost movable}$ Weyl nodal lines, we conclude that LaRhGe$_3$ supports a Weyl semimetallic state. We discover superconductivity in this compound with a $T_{\text c}$ of 0.39(1) K and $B_{\rm{c}}(0)$ of 2.2(1) mT, with evidence from specific heat and transverse-field muon spin relaxation. We find an exponential dependence in the normal state electrical resistivity below $\sim50$ K, while Seebeck coefficient and thermal conductivity measurements each reveal a prominent peak at low temperatures, indicative of strong electron-phonon interactions. To this end, we examine the temperature-dependent Raman spectra of LaRhGe$_3$ and find that the lifetime of the lowest energy $A_1$ phonon is dominated by phonon-electron scattering instead of anharmonic decay. We conclude that LaRhGe$_3$ has strong electron-phonon coupling in the normal state, while the superconductivity emerges from weak electron-phonon coupling. These results open up the investigation of electron-phonon interactions in the normal state of superconducting non-centrosymmetric Weyl semimetals.