Based on a microscopic model, we conducted a systematic theoretical study of the superconducting proximity effect and inverse proximity effect in heterostructures composed of Weyl semimetals (WSMs) and conventional s-wave superconductors. Through self-consistent calculations, we obtained the spatial distribution and symmetry properties of the superconducting order parameters. In the WSMs layer, the \( C_4 \) rotational symmetry and inversion symmetry of the superconducting order parameter are significantly broken, and the singlet-channel order parameter exhibits \( C_4 \) symmetry, containing both s-wave and d-wave components. By calculating the spectral functions and local density of states (LDOS) in the WSMs and conventional s-wave superconductors layers, we provided theoretical predictions that can be used to experimentally probe the proximity effects. In the conventional s-wave superconductors layer, the normal-state Fermi surface undergoes splitting due to interfacial coupling, with the degree of splitting increasing as the coupling strength grows, while an effective spin-orbit interaction term is induced. In the superconducting state, the original s-wave order parameter in the conventional s-wave superconductors is significantly suppressed, its symmetry is broken, and an additional d-wave pairing component is induced. These phenomena can be well understood by analyzing the Fermi surface characteristics of the original systems.
