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We investigate the possible occurrence of field-effect inducedsuperconductivity in the hydrogenated $(111)$ diamond surface byfirst-principles calculations. By computing the band alignment between bulkdiamond and the hydrogenated surface we show that the electric field exfoliatesthe sample, separating the electronic states at the valence band top from thebulk projected ones. At the hole doping values considered here, ranging from$n=2.84\times10^{13}$cm$^{-2}$ to $n=6\times 10^{14} $ cm$^{-2}$, the valenceband top is composed of up to three electronic bands hosting holes withdifferent effective masses. These bands resemble those of the undoped surface,but they are heavily modified by the electric field and differ substantiallyfrom a rigid doping picture. We calculate superconducting properties byincluding the effects of charging of the slab and of the electric field on thestructural properties, electronic structure, phonon dispersion andelectron-phonon coupling. We find that at doping as large as $n=6\times 10^{14}$ cm$^{-2}$, the electron-phonon interaction is $\lambda=0.81$ andsuperconductivity emerges with $T_{\text{C}}\approx 29-36$K. Superconductivityis mostly supported by in-plane diamond phonon vibrations and to a lesserextent by some out-of-plane vibrations. The relevant electron-phonon scatteringprocesses involve both intra and interband scattering so that superconductivityis multiband in nature.

Electric field exfoliation and high-T$_{\text{C}}$ superconductivity in field-effect hole-doped hydrogenated diamond (111)