In-plane sliding ferroelectricity and piezoelectricity in bilayer and trilayer g−C3N4

The graphenelike form of carbon nitride is known as$g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$, a single sheet of which may be composed of an $s$-triazine ($S$-type) or tri-$s$-triazine ($T$-type) periodic lattice with a different size of hole. By employing the first-principles calculation, we find that the difference in the out of plane polarization caused by the symmetry breaking of the $S$-type or $T$-type structure of bilayer $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ through interlayer sliding may be related to the size of the in-plane hole. The nonpolar bilayer $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ ($S$- or $T$-type) state needs to slide about two bond lengths before it is electrically driven to the polar state, resulting in ferroelectric structures with opposite polarization directions. It has been confirmed experimentally and theoretically [Zelisko et al., Nat. Commun. 5, 4284 (2014)] that the anomalous piezoelectric properties of $T$-type $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ monolayer come from their noncentrosymmetric triangular holes. Interestingly, we find here that the $S$-type $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ exhibits the opposite piezoelectric property to the $T$-type $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$, that is, a negative longitudinal piezoelectricity (NLP). Our computational analysis shows that the superposition of two reversed triangular holes in the $S$-type $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ plane will result in the emergence of NLP. Hence, the origin of different piezoelectric properties between $S$-type and $T$-type $g\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ is comparatively elucidated. These results provide alternative structural manipulation degrees of freedom for the inherent properties of two-dimensional van der Waals layered semiconductor materials, and expand ferroelectric candidate materials for next-generation nanoelectronic devices.