  The polarization response of a material to a strain gradient, known as
flexoelectricity, holds great promise for novel electromechanical applications.
Despite considerable recent progress, however, the effect remains poorly
understood. From both the fundamental and practical viewpoints, it is of
crucial importance to know whether the coupling coefficients are primarily
governed by the properties of the bulk material or by the details of the sample
surface. Here we provide, by means of first-principles calculations,
quantitative evidence supporting the latter scenario. In particular, we
demonstrate that a SrTiO$_3$ film can yield a positive or negative
flexoelectric voltage depending on its surface termination. This result points
to a full control of the flexoelectric effect via surface/interface
engineering, opening exciting new avenues for device design.
