  In view of the recent progress in experiments on charge transport through
various Josephson junctions made out of graphene, we have made a careful
comparison between the theory and some of the available experimental results.
Within the framework of a transfer matrix approach, we have first analytically
derived the spectrum of Andreev bound states (ABS) in a superconductor
-graphene-superconductor (SGS) junction for a wide range of experimentally
relevant parameters. We have particularly considered the case of monolayer
graphene (MLG). The theoretical results can account for both the retro Andreev
reflection (RAR) and the specular Andreev reflection (SAR) in the relevant
parameter range. Using the ABS spectrum we have evaluated the current through
such junctions and the junction conductance from the analytically derived
expressions at different bias voltages for a range of other system parameters
directly taken from the experimental works. These theoretical results have then
been compared with experimental results. Evaluated current and the conductance
show scaling behaviour with change in the junction length and agree well with
the experimental results. In the relevant parameter regime where the SAR
process is dominant, the calculated values of the current and the conductivity
have been found much lower than the corresponding values observed when the RAR
process is dominant.
