  A centrosymmetric stress cannot induce a polar response in centric materials,
piezoelectricity is, for example, possible only in non-centrosymmetric
structures. An exception is meta-materials with shape asymmetry, which may be
polarized by stress even when the material is centric. In this case the
mechanism is flexoelectricity, which relates polarization to a strain gradient.
The flexoelectric response scales inversely with size, thus a large effect is
expected in nanoscale materials. Recent experiments in polycrystalline,
centrosymmetric perovskites [e.g., (Ba,Sr)TiO3] have indicated values of
flexoelectric coefficients that are orders of magnitude higher than
theoretically predicted, promising practical applications based on bulk
materials. We show that materials with unexpectedly large flexoelectric
response exhibit breaking of the macroscopic centric symmetry through
inhomogeneity induced by the high temperature processing. The emerging
electro-mechanical coupling is significant and may help to resolve the
controversy surrounding the large apparent flexoelectric coefficients in this
class of materials.
