  We investigated the electrical transport properties of
superconductor-graphene-superconductor (SGS) Josephson junctions. In low
voltage bias, we observed conventional proximity-coupled Josephson effect, such
as the supercurrent flow through the graphene, sub-gap structure of
differential conductance due to Andreev reflection, and periodic modulation of
the critical current Ic with perpendicular magnetic field H to the graphene. In
high bias above the superconducting gap voltage, however, we also observed an
anomalous jump of the differential conductance, the voltage position of which
is sensitive to the backgate voltage Vg. Our extensive study with varying Vg,
temperature, and H reveals that the above-gap structure takes place at a
characteristic power P*, which is irrespective of Vg for a given junction.
Temperature and H dependences of P* are well explained by the increase of the
electron temperature in graphene.
