First-principles theory and calculation of flexoelectricity

We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and lattice contributions. We introduce practical supercell-based methods for calculating the flexoelectric coefficients from first principles, and demonstrate them by computing the coefficients for a variety of cubic insulating materials including C, Si, MgO, NaCl, CsCl, BaZrO₃, BaTiO₃, PbTiO₃, and SrTiO₃.