  The flexoelectric and electronic properties of zig-zag graphene nanoribbons
are explored under mechanical bending using state of the art first principles
calculations. A linear dependence of the bending induced out of plane
polarization on the applied strain gradient is found. The inferior
flexoelectric properties of graphene nanoribbons can be improved by more than
two orders of magnitude by hydrogen and fluorine functionalization (CH and CF
nanoribbons). A large out of plane flexoelectric effect is predicted for CF
nanoribbons. The origin of this enhancement lies in the electro-negativity
difference between carbon and fluorine atoms, which breaks the out of plane
charge symmetry even for a small strain gradient. The flexoelectric effect can
be further improved by co-functionalization with hydrogen and fluorine (CHF
Janus-type nanoribbon), where a spontaneous out of plane dipole moment is
formed even for flat nanoribbons. We also find that bending can control the
charge localization of valence band maxima and therefore enables the tuning of
the hole effective masses and band gaps. These results present an important
advance towards the understanding of flexoelectric and electronic properties of
hydrogen and fluorine functionalized graphene nanoribbons, which can have
important implications for flexible electronic applications.
