  Flexoelectricity is a universal electromechanical coupling effect whereby all
dielectric materials polarize in response to strain gradients. In particular,
nanoscale flexoelectricity promises exotic phenomena and functions, but
reliable characterization methods are required to unlock its potential. Here,
we report anomalous mechanical control of quantum tunnelling that allows for
characterizing nanoscale flexoelectricity. By applying strain gradients with an
atomic force microscope tip, we systematically polarize an ultrathin film of
otherwise nonpolar SrTiO$_{3}$, and simultaneously measure tunnel current
across it. The measured tunnel current exhibits critical behaviour as a
function of strain gradients, which manifests large modification of tunnel
barrier profiles via flexoelectricity. Further analysis of this critical
behaviour reveals significantly enhanced flexocoupling strength in ultrathin
SrTiO$_{3}$, compared to that in bulk, rendering flexoelectricity more potent
at the nanoscale. Our study not only suggests possible applications exploiting
dynamic mechanical control of quantum effect, but also paves the way to
characterize nanoscale flexoelectricity.
