Strong electron-phonon coupling and phonon-induced superconductivity in tetragonal C3N4 with hole doping

${\mathrm{C}}_{3}{\mathrm{N}}_{4}$ is a recently discovered phase of carbon nitrides with the tetragonal crystal structure [D. Laniel et al., Adv. Mater. (2023), doi:10.1002/adma.202308030] that is stable at ambient conditions. ${\mathrm{C}}_{3}{\mathrm{N}}_{4}$ is a semiconductor exhibiting flat-band anomalies in the valence band, suggesting the emergence of many-body instabilities upon hole doping. Here, using state-of-the-art first-principles calculations we show that hole-doped ${\mathrm{C}}_{3}{\mathrm{N}}_{4}$ reveals strong electron-phonon coupling, leading to the formation of a gapped superconducting state. The phase transition temperatures turn out to be strongly dependent on the hole concentration. We propose that holes could be injected into ${\mathrm{C}}_{3}{\mathrm{N}}_{4}$ via boron doping which induces, according to our results, a rigid shift of the Fermi energy without significant modification of the electronic structure. Based on the electron-phonon coupling and Coulomb pseudopotential calculated from first principles, we conclude that the boron concentration of 6 atoms per ${\mathrm{nm}}^{3}$ would be required to reach the critical temperature of $\ensuremath{\sim}36$ K at ambient pressure.