Quasiclassical Theory of the Josephson Effect in Ballistic Graphene Junctions

Abstract

The stationary Josephson effect in a system of ballistic graphene is studied in the framework of quasiclassical Green's function theory. Reflecting the ultimate two-dimensionality of graphene, a Josephson junction involving a graphene sheet embodies what we call a planar Josephson junction, in which superconducting electrodes partially cover the two-dimensional graphene layer, achieving a planar contact with it. For capturing this feature we employ a model of tunneling Hamiltonian that also takes account of the effects of inhomogeneous carrier density. Within the effective mass approximation we derive a general formula for the Josephson current, revealing characteristic features of the superconducting proximity effect in the planar Josephson junction. The same type of analysis has been equally applied to mono-, bi- and arbitrary $N$-layer cases.

arXiv comment13 pages, 5 figures, to appear in J. Phys. Soc. Jpn

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Cited by in corpus (9)

• Proximity coupling in superconductor-graphene heterostructures
• Josephson effect in a Weyl SNS junction
• Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping
• 1/f critical current noise in short ballistic graphene Josephson junctions
• Magnetic field oscillations of the critical current in long ballistic graphene Josephson junctions
• The dc Josephson current in a long multi-channel quantum wire
• Superconducting proximity effect on a two-dimensional Dirac electron system
• Effect of dilute impurities on short graphene Josephson junctions
• Unified Formula for Stationary Josephson Current in Planar Graphene Junctions