Josephson effect in ballistic graphene

We solve the Dirac–Bogoliubov–de Gennes equation in an impurity-free superconductor–normal-metal– superconductor junction, to determine the maximal supercurrent Ic that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result Ic W /L e 0 / is determined by the superconducting gap 0 and by the aspect ratio of the junction length L small relative to the width W and to the superconducting coherence length . Moving away from the Dirac point of zero doping, we recover the usual ballistic result Ic W / F e 0 / , in which the Fermi wavelength F takes over from L. The product IcRN 0 /e of the critical current and normal-state resistance retains its universal value up to a numerical prefactor on approaching the Dirac point.