Inspired by the successful synthesis of two-dimensional (2D) ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{WSi}}_2{\mathrm{N}}_4$ [Y. L. Hong et al., Science 369, 670 (2020)], which demonstrates that Si-N layers can act as effective modification layers on 2D materials, we investigate superconductivity and charge density waves (CDWs) of hexagonal boron nitride $\left(h\text{−}\mathrm{BN}\right)$ passivated with a Si-N layer based on first-principles calculations. Our results demonstrate that $h$-BN undergoes a transition from an insulator to a phonon-mediated superconductor with the transition temperature $\left(T_c\right)$ of 14.3 K when it is functionalized with a Si-N layer on one side. The electron-phonon coupling (EPC) of ${\mathrm{BN}}_2\mathrm{Si}$ is primarily attributed to the coupling between electrons in N-$p_z$ orbitals and the low-frequency in-plane vibrational modes of Si and N atoms, as well as higher-frequency out-of-plane vibration modes of N and B atoms. By applying $5\%$ biaxial tensile strain, the EPC constant $\lambda$ increases from 0.66 to 1.82, resulting in a significantly enhanced $T_c$ of 34.9 K. However, when the biaxial tensile strain reaches $6\%$, an obvious soft mode emerges in the lowest acoustic branch of phonon curves, indicating the presence of a CDW. The origin of the instabilities is analyzed based on Lindhard electron susceptibility and the phonon linewidths, revealing that the CDW is driven by both Fermi-surface nesting and EPC. Thus, the predicted ${\mathrm{BN}}_2\mathrm{Si}$ presents a promising platform for exploring 2D superconductivity and CDWs.

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• Charge density waves
• Superconductivity
• 2-dimensional systems
• Hexagonal boron nitride
• Density functional calculations
• Eliashberg theory