  The two-dimensional spin-imbalanced Fermi gas subject to s-wave pairing and
spin-orbit coupling is considered a promising platform for realizing a
topological chiral-p-wave superfluid. In the BCS limit of s-wave pairing, i.e.,
when Cooper pairs are only weakly bound, the system enters the topological
phase via a second-order transition driven by increasing the Zeeman
spin-splitting energy. Stronger attractive two-particle interactions cause the
system to undergo the BCS-BEC crossover, in the course of which the topological
transition becomes first-order. As a result, topological and nontopological
superfluids coexist in spatially separated domains in an extended region of
phase space spanned by the strength of s-wave interactions and the Zeeman
energy. Here we investigate this phase-coexistence region theoretically using a
zero-temperature mean-field approach. Exact numerical results are presented to
illustrate basic physical characteristics of the coexisting phases and to
validate an approximate analytical description derived for weak spin-orbit
coupling. Besides extending our current understanding of spin-imbalanced
superfluid Fermi systems, the present approach also provides a platform for
future studies of unconventional Majorana excitations that, according to
topology, should be present at the internal interface between coexisting
topological and nontopological superfluid parts of the system.
