Phase Stability and Anisotropic Superconductivity in Ternary M2B4C2 (M=Ca, Mg) Monolayer

In this work, we investigate the phase stability, electronic structure, and superconducting properties of the two-dimensional ternary borocarbides MB${}_4$C${}_2$ (M = Ca, Mg) using first-principles calculations and fully anisotropic Migdal-Eliashberg theory. Ab initio molecular dynamics, phonon dispersion, and elastic constant calculations confirm that both monolayers are dynamically, thermally, and mechanically stable. Electronic structure analysis reveals an intrinsic metallic nature with a multiband Fermi surface, where states near the $\mathrm{\Gamma }$ point are dominated by in-plane B-$p_x$, $p_y$ orbitals, while zone-boundary states are primarily derived from out-of-plane B-$p_z$ orbitals. The electron-phonon coupling is determined to be $\lambda =0.64$ for both materials, driven by the rigid covalent B-B and B-C honeycomb networks. By solving the anisotropic Eliashberg equations, we predict that CaB${}_4$C${}_2$ and MgB${}_4$C${}_2$ are nodeless two-gap superconductors with critical temperatures ($T_c$) of 33.4 K and 33.8 K, respectively, at a Coulomb pseudopotential of $\mu =0.10$. Furthermore, the superconducting state remains robust under increased Coulomb repulsion ($\mu =0.13$), retaining elevated $T_c$ values of 31.2 K and 30.9 K, respectively. These findings establish MB${}_4$C${}_2$ monolayers as promising candidates for nanoscale superconducting applications and enrich the family of two-dimensional multigap superconductors.