  In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was
realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which
represents an important step forward in the study of synthetic gauge field
using cold atoms. In the experiment, it was shown that a Raman-induced
two-dimensional SOC exists in the dressed-state basis close to a Dirac point of
the single-particle spectrum. By contrast, the short-range inter-atomic
interactions of the system are typically expressed in the hyperfine-spin basis.
The interplay between synthetic SOC and interactions can potentially lead to
interesting few- and many-body phenomena but has so far eluded theoretical
attention. Here we study in detail properties of two-body bound states of such
a system. We find that, due to the competition between SOC and interaction, the
stability region of the two-body bound state is in general reduced.
Particularly, the threshold of the lowest two-body bound state is shifted to a
positive, SOC-dependent scattering length. Furthermore, the center-of-mass
momentum of the lowest two-body bound state becomes nonzero, suggesting the
emergence of Fulde-Ferrell pairing states in a many-body setting. Our results
reveal the critical difference between the experimentally realized
two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an
interacting system, and paves the way for future characterizations of
topological superfluid states in the experimentally relevant systems.
