Model Calculation of the Piezoelectric Coefficient of Hexagonal 2D Materials

摘要： A quantum-mechanical microscopic model of the piezoelectric e?ect in 2D materials is developed. The piezoelectric coe?cient requires the calculation of an internal atomic displacement and an e?ective piezoelectric charge. The internal displacement is obtained from minimizing the strain energy given by a Keating-like model, while the e?ective 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 ?nal theory only requires atomic energies and the elasticity constants of the materials as input parameters. The piezoelectric coe?cients of a number of II-VI, 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 ?rst time.