  We study a two-dimensional heterostructure comprised of a monolayer of the
magnetic insulator chromium triiodide (CrI$_3$) on a superconducting lead (Pb)
substrate. Through first-principles computation and a tight-binding model, we
demonstrate that charge transfer from the Pb substrate dopes the CrI$_3$ into
an effective half-metal, allowing for the onset of a gapless topological
superconductivity phase via the proximity effect. This phase, in which there
exists a superconducting gap only in part of the Fermi surface, is shown to
occur generically in 2D half-metal-superconductor heterostructures which lack
two-fold in-plane rotational symmetry. However, a sufficiently large
proximity-induced pairing amplitude can bring such a system into a fully-gapped
topological superconducting phase. As such, these results are expected to
better define the optimal 2D component materials for future proposed TSC
heterostructures.
