Graphene-based superconducting quantum point contacts

Abstract

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 I_c is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers, I_c decreases monotonically with lowering W/L and tends to a constant minimum for a narrow nanoribbon with $W\lesssim{}L$. The minimum I_c is zero for the smooth edges but $e\Delta_{0}/\hbar$ 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 I_cR_N 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, I_c is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.