  The dc Josephson effect is investigated in a single-walled metallic carbon
nanotube connected to two superconducting leads. In particular, by using the
Luttinger liquid theory, we analyze the effects of the electron-electron
interaction on the supercurrent. We find that in the long junction limit the
strong electronic correlations of the nanotube, together with its peculiar band
structure, induce oscillations in the critical current as a function of the
junction length and/or the nanotube electron filling. These oscillations
represent a signature of the Luttinger liquid physics of the nanotube, for they
are absent if the interaction is vanishing. We show that this effect can be
exploited to reverse the sign of the supercurrent, realizing a tunable
\pi-junction.
