Proximity effect of $s$-wave superconductor on an inversion-broken Weyl semimetal

Inducing superconductivity in systems with unconventional band structures is a promising approach for realizing unconventional superconductivity. Of particular interest are single-interface or Josephson junction architectures involving Weyl semimetals (WSM), which are predicted to host odd-parity, potentially topological, superconducting states. These expectations rely crucially on the tunneling of electronic states at the interface between the two systems. In this study, we revisit the question of induced superconductivity in an inversion-broken WSM via quantum tunneling, treating the interface as an effective potential barrier. We determine the conditions under which the gap function couples to the Weyl physics and its properties within the WSM. Our simulations show that the mismatch in the nature of the low-energy electronic states leads to a rapid decay of the superconductivity within the semimetal.