  We develop theory models for both ballistic and disordered superconducting
monolayer black phosphorus devices in the presence of magnetic exchange field
and strain. The ballistic case is studied through a microscopic Bogoliubov-de
Gennes formalism while for the disordered case we formulate a quasiclassical
model. Utilizing the two models, we theoretically study the response of
supercurrent to an externally applied magnetic field in two-dimensional black
phosphorus Josephson junctions. Our results demonstrate that the response of
the supercurrent to a perpendicular magnetic field in ballistic samples can
deviate from the standard Fraunhofer interference pattern when the Fermi level
and mechanical strain are varied. This finding suggests the combination of
chemical potential and strain is an efficient external knob to control the
current response in highly sensitive strain-effect transistors and
superconducting quantum interference devices. We also study the supercurrent in
a superconductor-ferromagnet-ferromagnet-superconductor junction where the
magnetizations of the two adjacent magnetized regions are uniform with
misaligned orientations. We show that the magnetization misalignment can
control the excitation of harmonics higher than the first harmonic sin(phi) (in
which phi is the phase difference between the superconductors) in supercurrent
and constitutes a full spin switching current element. Finally, we discuss
possible experimental implementations of our findings. We foresee our models
and discussions could provide guidelines to experimentalists in designing
devices and future investigations.
