  Many-body transport has emerged as an efficient tool for understanding
interaction effects in quantum materials with a multi-band electronic
structure. This paper proposes a formula for the two-particle transmission
coefficient for Cooper-pair transport between multi-band normal and
superconducting materials. The approach employs a tight-binding nonequilibrium
Green's function technique, allowing a direct calculation of the two-particle
current, without invoking the paradigm of Andreev reflection. As an application
of the theory, we demonstrate a low-field linear magnetoresistance effect for
superconductors with an induced nonunitary order parameter. These results
uncover an unexplored route for detecting unconventional nonunitary
superconductivity in quantum materials of current theoretical and experimental
interest.
