Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

Flexoelectricity is an electromechanical phenomenon produced in a dielectric material, with or without centrosymmetric microstructure, undergoing non-uniform strain. It characterized by the fourth-order flexoelectric tensor, which links electric polarization vector gradient of second-order strain tensor. Our previous work [H. Le Quang and Q.-C. He, Proc. R. Soc. A 467, 2369 (2011)] solved fundamental theoretical problem determining number types all rotational symmetries that tensor can exhibit. In present study, compact explicit matrix representations are provided so as to facilitate use it any possible symmetry. The reflection have also determined. To identify symmetry given simple efficient graphic method based on concept pole figures presented illustrated.