  We investigate the unusual features of the quantum transport in gapped
monolayer graphene, which is in a pseudospin symmetry-broken state with a net
perpendicular pseudomagnetization. Using these pseudoferromagnets (PFs), we
propose a perfect pseudospin valve effect that can be used for realizing
pseudospintronics in monolayer graphene. The peculiarity of the associated
effects of pseudo spin injection and pseudo spin accumulation are also studied.
We further demonstrate the determining effect of the sublattice pseudospin
degree of freedom on Andreev reflection and the associated proximity effect in
hybrid structures of PFs and a superconductor in S/PF and PF/S/PF geometries.
In particular, we find a peculiar Andreev reflection that is associated with an
inversion of the z component of the carriers pseudospin vector. Our results
show that the gapped normal graphene behaves like a ferromagnetic graphene and
the effect of the pseudospin degree of freedom in gapped graphene is as
important as the spin in a ferromagnetic graphene.
