  We report a theoretical/experimental study of current-voltage characteristics
(I-V) of graphene devices near the Dirac point. The I-V can be described by a
power law (I \propto V^\alpha, with 1< \alpha <= 1.5). The exponent is higher
when the mobility is lower. This superlinear I-V is interpreted in terms of the
interplay between Zener-Klein transport, that is tunneling between different
energy bands, and defect scattering. Surprisingly, the Zener-Klein tunneling is
made visible by the presence of defects.
