Migdal-Eliashberg theory of multi-band high-temperature superconductivity in field-effect-doped hydrogenated (111) diamond

[Display omitted] •High-Tc superconductivity expected at ~6 × 1014 cm−2 field-induced hole density.•Single-band Migdal-Eliashberg theory predicts Tc~40 K with a gap ratio 3.72.•The multi-band pairing increases the Tc between ~4% and ~8%.•The quasi-particle DOS shows three distinct peaks, one for each superconducting gap.•Intra-band couplings dominate the total pairing with respect to inter-band ones. We perform single- and multi-band Migdal-Eliashberg (ME) calculations with parameters exctracted from density functional theory (DFT) simulations to study superconductivity in the electric-field-induced 2-dimensional hole gas at the hydrogenated (111) diamond surface. We show that according to the Eliashberg theory it is possible to induce a high-Tc superconducting phase when the system is field-effect doped to a surface hole concentration of 6×1014 cm−2, where the Fermi level crosses three valence bands. Starting from the band-resolved electron-phonon spectral functions α2Fjj′(ω) computed ab initio, we iteratively solve the self-consistent isotropic Migdal-Eliashberg equations, in both the single-band and the multi-band formulations, in the approximation of a constant density of states at the Fermi level. In the single-band formulation, we find Tc≈40 K, which is enhanced between 4% and 8% when the multi-band nature of the system is taken into account. We also compute the multi-band-sensitive quasiparticle density of states to act as a guideline for future experimental works.