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Starting from first principles, we show the formation and evolution ofsuperconducting gaps in MgB$_2$ at its ultrathin limit. Atomically thin MgB$_2$is distinctly different from bulk MgB$_2$ in that surface states becomecomparable in electronic density to the bulk-like $\sigma$- and $\pi$-bands.Combining the ab initio electron-phonon coupling with the anisotropicEliashberg equations, we show that monolayer MgB$_2$ develops three distinctsuperconducting gaps, on completely separate parts of the Fermi surface due tothe emergent surface contribution. These gaps hybridize nontrivially with everyextra monolayer added to the film, owing to the opening of additional couplingchannels. Furthermore, we reveal that the three-gap superconductivity inmonolayer MgB$_2$ is robust over the entire temperature range that stretches upto a considerably high critical temperature of 20 K. The latter can be boostedto $>$50 K under biaxial tensile strain of $\sim$ 4\%, which is an enhancementstronger than in any other graphene-related superconductor known to date.

Evolution of multi-gap superconductivity in the atomically thin limit: Strain-enhanced three-gap superconductivity in monolayer MgB$_2$