  We study the phase diagram in a two-dimensional Fermi gas with the synthetic
spin-orbit coupling that has recently been realized experimentally. In
particular, we characterize in detail the properties and the stability region
of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in such a
system, which are induced by spin-orbit coupling and Fermi surface asymmetry.
We identify several distinct nodal FFLO states by studying the topology of
their respective gapless contours in momentum space. We then examine the phase
structure and the number density distributions in a typical harmonic trapping
potential under the local density approximation. Our studies provide detailed
information on the FFLO pairing states with spin-orbit coupling and Fermi
surface asymmetry, and will facilitate experimental detection of these
interesting pairing states in the future.
