Interplay of Superconductivity, Ferromagnetism, and Half-Metallicity in Gated Single-Layer g-C₃N₄

Graphitic carbon nitride (g-C₃N₄) hosts lone pairs arising from broken carbon-nitrogen bonds in its heptazine structure. These strongly localized and weakly hybridized states form ultraflat bands, potentially leading to correlated states when doped. Using first-principles calculations, we show that field-effect hole doping in single-layer g-C₃N₄ depletes these lone pairs, unveiling a rich phase diagram with a complex interplay of superconducting, half-metallic, and insulating ferromagnetic phases, even at very low charging and in the absence of transition metal ions. Our work highlights gated two-dimensional systems hosting lone pairs as a novel platform for strongly correlated states.