Josephson effect in mesoscopic graphene strips with finite width

Ali G. Moghaddam; Malek Zareyan

doi:10.1103/PhysRevB.74.241403

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Josephson effect in mesoscopic graphene strips with finite width

Ali G. Moghaddam, Malek Zareyan

DOI 10.1103/PhysRevB.74.241403 · Physical Review B

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Abstract

We study Josephson effect in a ballistic graphene strip of length L smaller than the superconducting coherence length and arbitrary width W. We find that the dependence of the critical supercurrent Ic on W is drastically different for different types of the edges. For smooth and armchair edges at low concentration of the carriers Ic decreases monotonically with decreasing W∕L and tends to a constant minimum for a narrow strip W∕L≲1. The minimum supercurrent is zero for smooth edges but has a finite value eΔ0∕ℏ for the armchair edges. At higher concentration of the carriers, in addition to this overall monotonic variation, the critical current undergoes a series of peaks with varying W. On the other hand in a strip with zigzag edges the supercurrent is half-integer quantized to (n+1∕2)4eΔ0∕ℏ, showing a stepwise variation with W.