  The interplay between quantum Hall states and Cooper pairs is usually
hindered by the suppression of the superconducting state due to the strong
magnetic fields needed to observe the quantum Hall effect. From this point of
view graphene is special since it allows the creation of strong pseudo-magnetic
fields due to strain. We show that in a Josephson junction made of strained
graphene, Cooper pairs will diffuse into the strained region. The pair
correlation function will be sub-lattice polarized due to the polarization of
the local density of states in the zero pseudo-Landau level. We uncover two
regimes; 1) one in which the cyclotron radius is larger than the junction
length in which case the supercurrent will be enhanced, and 2) the long
junction regime where the supercurrent is strongly suppressed because the
junction becomes an insulator. In the latter case quantized Hall states form
and Andreev scattering at the normal/superconducting interface will induce edge
states. Our numerical calculation has become possible due to an extension of
the Chebyshev Bogoliubov-de Gennes method to computations on video cards
(GPUs).
