  Two-dimensional materials are of interest for their exotic properties, for
example, superconductivity, and highly tunability. Focusing on phonon-mediating
superconductivity, one would propose to promote critical temperature by
substituting heavy elements by lighter ones, in order to increase Debye
temperature. Following recent experimental progress in transition-metal
nitrides and theoretically revealing W$_2$N$_3$ as a candidate for
high-temperature superconductivity, we investigate the possibility of
two-dimensional superconductivity through surface engineering on MoN$_2$. Using
density functional theory calculation, we found multigap superconductivity at
temperature up to 36K within anisotropic Eliashberg equation in passivated
electride-like surfaces. We also demonstrate their possibility to sustain
topological superconductivity with strong spin-orbital coupling.
