  Superconductivity is significantly enhanced in monolayer FeSe grown on
SrTiO3, but not for multilayer films, in which large strength of nematicity
develops. However, the link between the high-transition temperature
superconductivity in monolayer and the correlation related nematicity in
multilayer FeSe films is not well understood. Here, we use low-temperature
scanning tunneling microscopy to study few-layer FeSe thin films grown by
molecular beam epitaxy. We observe an incommensurate long-range smectic phase,
which solely appears in bilayer FeSe films. The smectic order still locally
exists and gradually fades away with increasing film thickness, while it
suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase
transition. Surface alkali-metal doping can suppress the smectic phase and
induce high-Tc superconductivity in bilayer FeSe. Our observations provide
evidence that the monolayer FeSe is in close proximity to the smectic phase,
and its superconductivity is likely enhanced by this electronic instability as
well.
