  We investigate the zero-bias behavior of Josephson junctions made of
encapsulated graphene boron nitride heterostructures in the long ballistic
junction regime. For temperatures down to 2.7K, the junctions appear
non-hysteretic with respect to the switching and retrapping currents $I_C$ and
$I_R$. A small non-zero resistance is observed even around zero bias current,
and scales with temperature as dictated by the phase diffusion mechanism. By
varying the graphene carrier concentration we are able to confirm that the
observed phase diffusion mechanism follows the trend for an overdamped
Josephson junction. This is in contrast with the majority of graphene-based
junctions which are underdamped and shorted by the environment at high
frequencies.
