  Proximity-induced superconductivity in fractional quantum Hall edges is a
prerequisite to proposed realizations of parafermion zero-modes. A recent
experimental work [G\"{u}l et al., Phys. Rev. X 12, 021057 (2022)] provided
evidence for such coupling, in the form of a crossed Andreev reflection signal,
in which electrons enter a superconductor from one chiral mode and are
reflected as holes to another, counter-propagating chiral mode. Remarkably,
while the probability for crossed Andreev reflection was small, it was stronger
for $\nu=1/3$ fractional quantum Hall edges than for integer ones. We
theoretically explain these findings, including the relative strengths of the
signals in the two cases and their qualitatively different temperature
dependencies. An essential part of our model is the coupling of the edge modes
to normal states in the cores of Abrikosov vortices induced by the magnetic
field, which provide a fermionic bath. We find that the stronger crossed
Andreev reflection in the fractional case originates from the suppression of
electronic tunneling between the fermionic bath and the fractional quantum Hall
edges. Our theory shows that the mere observation of crossed Andreev reflection
signal does not necessarily imply the presence of localized parafermion
zero-modes, and suggests ways to identify their presence from the behavior of
this signal in the low temperature regime.
