  Baryons and cold dark matter (CDM) did not comove prior to recombination.
This leads to differences in the local baryon and CDM densities, the so-called
baryon-CDM isocurvature perturbations $\delta_{bc}$. These perturbations are
usually neglected in the analysis of Large-Scale Structure data but taking them
into account might become important in the era of high precision cosmology.
Using gravity-only 2-fluid simulations we assess the impact of such
perturbations on the dark matter halos distribution. In particular, we focus on
the baryon fraction in halos as a function of mass and large-scale
$\delta_{bc}$, which also allows us to study details of the nontrivial
numerical setup required for such simulations. We further measure the
cross-power spectrum between the halo field and $\delta_{bc}$ over a wide range
of mass. This cross-correlation is nonzero and negative which shows that halo
formation is impacted by $\delta_{bc}$. We measure the associated bias
parameter $b_{\delta_{bc}}$ and compare it to recent results, finding good
agreement. Finally we quantify the impact of such perturbations on the
halo-halo power spectrum and show that this effect can be degenerate with the
one of massive neutrinos for surveys like DESI.
