  Atmospheric escape is an important process that controls the long-term
evolution of close-in planets. We perform radiation hydrodynamics simulations
of photo-evaporation of exoplanets' atmospheres to study the effect of
photoelectric heating by far-ultraviolet (FUV) radiation. Specifically, we
consider a close-in hot Jupiter around a hot A-star. Hot main-sequence stars
emit not only extreme ultraviolet radiation but also FUV radiation, and thus
can drive strong atmospheric escape by photoelectric heating. We show that the
planetary atmosphere escapes at a rate as large as $\dot{M}\sim10^{14}\,
\mathrm{g}~{\rm sec}^{-1}$ if the atmosphere contains a small amount of dust
grains with the level of ten percent of the local interstellar medium. Close-in
planets around hot stars can lose a significant fraction of the atmosphere
during the long-term evolution. We quantify the amount of dust necessary for
causing photoevaporation. The dust-to-gas mass ratio of $10^{-4}$ is sufficient
to drive stronger atmospheric escape by FUV photoelectric heating than in the
case with only extreme ultraviolet radiation. We also explore the metallicity
dependence of the FUV-driven escape. The mass-loss rate increases with
increasing the atmosphere's metallicity because of the enhanced photoelectric
heating, but the stellar FUV flux decreases with increasing stellar
metallicity. We derive an accurate estimate for the mass-loss rate as a
function of FUV flux and metallicity, and of the planet's characteristics. The
FUV driven atmospheric escape may be a key process to understand and explain
the so-called sub-Jovian desert.
