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Critical Josephson current in ballistic superconductor-graphene systems

We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson-junctions. For low temperatures we find non-sinusoidal dependence of the supercurrent on the superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviation of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed by a diffusive or ballistic metal. The relation to other recent theoretical results on graphene Josephson junctions is pointed out and the possible experimental relevance of our work is considered as well.