  Based on the BTK theory, we investigate the tunneling conductance in a
uniaxially strained graphene-based normal metal (NG)/ barrier
(I)/superconductor (SG) junctions. In the present model, we assume that
depositing the conventional superconductor on the top of the uniaxially
strained graphene, normal graphene may turn to superconducting graphene with
the Cooper pairs formed by the asymmetric Weyl-Dirac electrons, the massless
fermions with direction-dependent velocity. The highly asymmetrical velocity,
vy/vx>>1, may be created by strain in the zigzag direction near the transition
point between gapless and gapped graphene. In the case of the highly
asymmetrical velocity, we find that the Andreev reflection strongly depends on
the direction and the current perpendicular to the direction of strain can flow
in the junction as if there was no barrier. Also, the current parallel to the
direction of strain anomalously oscillates as a function of the gate voltage
with very high frequency. Our predicted result is found as quite different from
the feature of the quasiparticle tunneling in the unstrained graphene-based
NG/I/SG conventional junction. This is because of the presence of the
direction-dependent-velocity quasiparticles in the highly strained graphene
system.
