Strained graphene Josephson junction with anisotropic d-wave superconductivity

•We investigate influence of anisotropic Fermi velocity on strained graphene Josephson junction.•The superconductivity is considered unconventional dd-wave pairing.•We carry out our goal by introducing a relevant form of DBdG spinors for Andreev excitations.•The results are completely different from those in unstrained and conventional superconductivity similar junction.•A gap opens in Andreev states with respect to non-zero incidence angle, where states have a period of 2ππ.

Effect of proximity-induced superconductivity in the new two-dimensional structures, as graphene and topological insulator on the Andreev bound states (ABSs) and Josephson supercurrent has attracted much efforts. Motivated by this subject, we study, in particular, the influence of anisotropic Fermi velocity and unconventional d  -wave pairing in a strained graphene-based superconductor/normal/ superconductor junction. Strain is applied in the zigzag direction of graphene sheet. In this process, effect of zero energy states and Fermi wavevector mismatch are investigated. It is shown, that strain up to 22% in graphene lattice differently affects Josephson currents in parallel and perpendicular directions of strain. Strain causes to exponentially decrease the supercurrent in the strain direction, whereas increase for other direction. We find that, in one hand, the ABSs strongly depend on strain and, on the other hand, a gap opens in the states with respect to non-zero incidence angle of quasiparticles, where a period of 2ππ is obtained for Andreev states. Moreover, we observe no gap for θs≠0, when the zero energy states (ZESs) occur in α=π/4α=π/4 due to anisotropic superconducting gap. In this case, ABSs have a period of 4ππ.S