Flat-band based high-temperature ferromagnetic semiconducting state in the graphitic C4N3 monolayer

Half-filled isolated flat-band paves a new way to realize high-temperature ferromagnetic semiconductor for spintronics applications, but it is extremely rare in lattice models and lacking in realistic materials. Herein, the 2 × 2 super-cell of the honeycomb lattice with a single-hole defect is proposed as a new lattice model (HL-D-1/8) to realize nontrivial isolated flat-bands. We further demonstrate that C₄N₃ monolayer of the experimentally realized graphitic carbon nitride (Adv. Mater., 22, 1004, 2010; Nat. Commun., 9, 3366, 2018) is a perfect system holding such a lattice to host flat-bands. A new corrugated Pca21 configuration is proposed as the ground state for the free-standing C₄N₃ monolayer, which is dynamically stable and energetically more favorable than the widely-used flat one without dynamical stability. The Pca21 configuration is found to be an intrinsic ferromagnetic half-semiconductor (T_c ≈ 241 K) with one semiconducting spin-channel (1.75 eV) and one insulating spin-channel (3.64 eV), which is quite rare in two-dimensional systems. Its ferromagnetic semiconducting property originates from the isolated p_z-state flat-band as the corrugation shifts the flat-band upward to the Fermi level. Interestingly, such a corrugated Pca21 C₄N₃ monolayer is found to be both piezoelectric and ferroelectric, which makes it an unusual metal-free two-dimensional multiferroic.