Towards a bulk theory of flexoelectricity.

Flexoelectricity is the linear response of polarization to a strain gradient. Here we address the simplest class of dielectrics, namely, elemental cubic crystals, and we prove that therein there is no extrinsic (i.e., surface) contribution to flexoelectricity in the thermodynamic limit. The flexoelectric tensor is expressed as a bulk response of the solid, manifestly independent of surface configurations. Furthermore, we prove that the flexoelectric responses induced by a long-wavelength phonon and by a uniform strain gradient are identical.