  The two-dimensional nature of graphene Josephson junctions offers the
possibility of creating effective superconductor-ferromagnet-superconductor
junctions with tunable Zeeman splitting caused by an in-plane magnetic field.
Such junctions would be able to alternate between a conventional
superconducting ground state and a ground state with an intrinsic phase
difference, making them controllable $0-\pi$ Josephson junctions. However, in
addition to the Zeeman splitting, an in-plane magnetic field will in general
also produce an orbital effect because of height variations in graphene,
colloquially known as ripples. Both the Zeeman and orbital effect will thus
affect the critical current, so to be able to identify $0-\pi$ transitions it
is necessary to understand their combined effect. From both analytical and
numerical solutions of the Usadel equation we find that ripples can in fact
produce a current response similar to that which is characteristic of a $0-\pi$
transition. Hence, additional analysis is required in order to reveal the
presence of a $0-\pi$ transition caused by spin-splitting in graphene with
ripples. We provide a closed form analytical expression for the critical
current in the presence of exchange field and ripple effects as well as an
expression for the scaling of critical current zeroes with junction parameters.
