  We study the effects of synthetic spin-orbit coupling on the pairing physics
in quasi-one-dimensional ultracold Fermi gases of alkaline-earth-metal-like
atoms near an orbital Feshbach resonance (OFR). The interplay between
spin-orbit coupling and pairing interactions near the OFR leads to an
interesting topological Fulde-Ferrell state, where the nontrivial topology of
the state is solely encoded in the closed channel with a topologically trivial
Fulde-Ferrell pairing in the open channel. We confirm the topological property
of the system by characterizing the Zak phase and the edge states. The
topological Fulde-Ferrell state can be identified by the momentum-space density
distribution obtained from time-of-flight images.
