Superconductor-graphene-superconductor Josephson junction in the quantum Hall regime

Abstract

Using a nonequilibrium-Green-function method, we numerically studied the transport properties of a superconductor-graphene-superconductor Josephson junction hybrid system in the quantum Hall regime. Our numerical calculations show that there are two interference patterns of the critical current due to the unique band structure of graphene. One is caused by the usual intraband Andreev retroreflection process, and the other one is caused by the interband specular Andreev reflection process. In the Andreev retroreflection regime, chiral Andreev edge states are formed and a distinct supercurrent can be observed. The critical current displays an AB oscillation behavior and the period is approximately 2Φ0=h/e. As for the specular Andreev refection process, the reflected holes are bent back to the reverse direction of the incident electrons and the supercurrent flows along both edges. It is similar to a superconductor ring Josephson junction and the period is Φ0=h/2e. However, the critical current for the specular Andreev reflection process is very small and is unlikely to be observable in an experiment. Thus, we conclude that our numerical calculations are inconsistent to the experimental findings by Amet et al. [Science 352, 966 (2016)].

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