Model of the piezoelectric coefficient of hexagonal two-dimensional materials

A quantum-mechanical microscopic model of the piezoelectric effect in two-dimensional materials is developed. The piezoelectric coefficient requires the calculation of an internal atomic displacement and an effective piezoelectric charge. The internal displacement is obtained from minimizing the strain energy given by a Keating-like model, while the effective charge takes into account the atomic displacements and also a redistribution of the electronic charge; a bond-orbital model is used to compute the latter. The final theory only requires atomic energies and the elasticity constants of the materials as input parameters. The piezoelectric coefficients of a number of II-V, III-V and IV-IV materials that could stably form in the planar hexagonal structure are computed; results for the IV-IV materials are obtained for the first time.