Gapped graphene-based Josephson junction with d-wave pair coupling

• We aim to study the influence of the Josephson current passing through a d-wave S/I/S gapped graphene-based junction.
• We investigate how the Andreev bound states and the Josephson current are affected by characteristic of d-wave pairing asymmetry.
• It is shown that the Josephson current for special range of phase vanishes and the position of the maximum current depends on the mass gap of graphene.

The Josephson current passing through a S/I/S gapped graphene-based junction, where superconductivity in the S region is induced by depositing unconventional d-wave superconductor is investigated. The energy levels of massive Dirac fermions are exactly found for Andreev bound states. We illustrate the effect of characteristic of d-wave pairing symmetry on the Andreev bound states and the Josephson current. It is shown that the Josephson current vanishes for special range of superconductivity phase, φ = φ1 − φ2 and the position of the maximum current depends on the mass gap of graphene. The critical supercurrent varies in an oscillatory manner as function of the barrier strength, so that the period of oscillations does not change by increasing the effective mass of quasiparticles.