Electronic structure, electron-phonon coupling, and superconductivity in noncentrosymmetric ThCoC2 from ab initio calculations

Superconductors without inversion symmetry in their crystal structure are known to exhibit unconventional properties. Recently, based on the measured temperature dependence of magnetic field penetration depth, superconductivity noncentrosymmetric $\mathrm{ThCoC_2}$ was proposed be a nodal $d$-wave and mediated by spin fluctuations. Moreover, non-BCS behavior electronic specific heat upper critical were reported. In this work, structure, phonons electron-phonon coupling studied basis \textit{ab initio} computations. The effect spin-orbit interaction is analyzed, large splitting band found. calculated constant $\lambda = 0.59$ remains decent agreement with experimental estimates, suggesting that strong enough explain $T_c \simeq 2.5$~K. Nevertheless, we show conventional isotropic Eliashberg formalism unable describe thermodynamic properties superconducting state, as depth deviate from experiments, which likely driven breaking. addition, shed more light pairing mechanism, propose measure carbon isotope effect, our calculations predict observation an exponent $\alpha 0.15$.