  Binary stars form from the same parent molecular cloud and thus have the same
chemical composition. Forming planets take building material (solids) away from
the surrounding protoplanetary disc. Assuming that the disc's accretion onto
the star is the main process that clears the disc, the atmosphere of the star
will show abundance reductions caused by the material accreted by the forming
planet(s). If planets are only forming around one star of a binary system, the
planet formation process can result in abundance differences in wide binary
stars, if their natal protoplanetary discs do not interact during planet
formation. Abundance differences in the atmospheres of wide binaries hosting
giant planets have already been observed and linked to the formation location
of giant planets. Here, we model how much building material is taken away for
super-Earth planets that form inside/outside of the water ice line as well as
ice giants forming inside/outside of the CO ice line. Our model predicts a
significant abundance difference $\Delta$[X/H] in the stellar atmospheres of
the planet-hosting binary component. Our model predicts that super-Earths that
form inside the water ice line ($r<r_{\rm H_2O}$) will result in an
$\Delta$[Fe/H]/$\Delta$[O/H] abundance difference in the their host star that
is a factor of 2 larger than for super-Earths formed outside the water ice line
($r>r_{\rm H_2O}$) in the water rich parts of the disc. Additionally, our model
shows that the $\Delta$[Fe/H]/$\Delta$[C/H] abundance difference in the host
star is at least a factor of 3 larger for ice giants formed at $r<r_{\rm CO}$
compared to ice giants formed far out in the protoplanetary disc ($r>r_{\rm
CO}$). Future observations of wide binary star systems hosting super-Earths and
ice giants could therefore help to constrain the migration pathway of these
planets and thus constrain planet formation theories.
