  It has been suggested that the occurrence rate of hot Jupiters (HJs) in open
clusters might reach several per cent, significantly higher than that of the
field ($\sim$ a per cent). In a stellar cluster, when a planetary system
scatters with a stellar binary, it may acquire a companion star which may
excite large amplitude von Zeipel-Lidov-Kozai oscillations in the planet's
orbital eccentricity, triggering high-eccentricity migration and the formation
of an HJ. We quantify the efficiency of this mechanism by modelling the
evolution of a gas giant around a solar mass star under the influence of
successive scatterings with binary and single stars. We show that the chance
that a planet $\in(1,10)$ au becomes an HJ in a Gyr in a cluster of stellar
density $n_*=50$ pc$^{-3}$ and binary fraction $f_\mathrm{bin}=0.5$ is about
2\% and an additional 4\% are forced by the companion star into collision with
or tidal disruption by the central host. An empirical fit shows that the total
percentage of those outcomes asymptotically reaches an upper limit determined
solely by $f_\mathrm{bin}$ (e.g., $10\%$ at $f_\mathrm{bin}=0.3$ and 18\% at
$f_\mathrm{bin}=1$) on a timescale inversely proportional to $n_*$ ($\sim$ Gyr
for $n_*\sim100$ pc$^{-3}$). The ratio of collisions to tidal disruptions is
roughly a few, and depends on the tidal model. Therefore, if the giant planet
occurrence rate is 10~\%, our mechanism implies an HJ occurrence rate of a few
times 0.1~\% in a Gyr and can thus explain a substantial fraction of the
observed rate.
