  Symmetry breaking at surfaces and interfaces and the capability to support
large strain gradients in nanoscale systems enable new forms of
electromechanical coupling. Here we introduce the concept of quantum
flexoelectricity, a phenomenon that is manifested when the mechanical
deformation of non-polar quantum systems results in the emergence of net dipole
moments and hence linear electromechanical coupling proportional to local
curvature. The concept is illustrated in carbon systems, including
polyacetylene and nano graphitic ribbons. Using density functional theory
calculations for systems made of up to 400 atoms, we determine the
flexoelectric coefficients to be of the order of ~ 0.1 e, in agreement with the
prediction of linear theory. The implications of quantum flexoelectricity on
electromechanical device applications, and physics of carbon based materials
are discussed.
