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We theoretically study spin-$1/2$ fermions confined to two spatial dimensionsand experiencing isotropic short-range attraction in the presence of bothspin-orbit coupling and Zeeman spin splitting - a prototypical system fordeveloping topological superfluidity in the many-body sector. Exact solutionsfor two-particle bound states are found to have a triplet contribution thatdominates over the singlet part in an extended region of parameter space wherethe combined Zeeman- and center-of-mass-motion-induced spin-splitting energy islarge. The triplet character of dimers is purest in the regime of weak $s$-waveinteraction strength. Center-of-mass momentum is one of the parametersdetermining the existence of bound states, which we map out for both two- andone-dimensional types of spin-orbit coupling. Distinctive features emerging inthe orbital part of the bound-state wave function, including but not limited toits $p$-wave character, provide observable signatures of unconventionalpairing.

Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting