Graphene-based superconducting quantum point contacts

We investigate the Josephson effect in the graphene nanoribbons of length L smaller than the superconducting coherence length and an arbitrary width W. We find that in contrast to an ordinary superconducting quantum point contact (SQPC), the critical supercurrent Ic is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers, Ic decreases monotonically with lowering W/L and tends to a constant minimum for a narrow nanoribbon with W<or similar L. The minimum Ic is zero for the smooth edges but eΔ0/ℎ for the armchair edges. At higher concentrations of the carriers this monotonic variation acquires a series of peaks. Further analysis of the current-phase relation and the Josephson coupling strength IcRN in terms of W/L and the concentration of carriers revels significant differences with those of an ordinary SQPC. On the other hand for a zigzag nanoribbon, we find that, similar to an ordinary SQPC, Ic is quantized but to the half-integer values (n+1/2)4eΔ0/ℎ. (orig.)