A chiral quantum Hall (QH) edge state placed in proximity to an s-wave
superconductor experiences induced superconducting correlations. Recent
experiments have observed the effect of proximity-coupling in QH edge states
through signatures of the mediating process of Andreev reflection. We present
the microscopic theory behind this effect by modeling the system with a
many-body Hamiltonian, consisting of an s-wave superconductor, subject to
spin-orbit coupling and a magnetic field, which is coupled by electron
tunneling to a QH edge state. By integrating out the superconductor we obtain
an effective pairing Hamiltonian in the QH edge state. We clarify the
qualitative appearance of nonlocal superconducting correlations in a chiral
edge state and analytically predict the suppression of electron-hole conversion
at low energies (Pauli blocking) and negative resistance as experimental
signatures of Andreev reflection in this setup. In particular, we show how two
surface phenomena of the superconductor, namely Rashba spin-orbit coupling and
a supercurrent due to the Meissner effect, are essential for the Andreev
reflection. Our work provides a promising pathway to the realization of
Majorana zero-modes and their parafermionic generalizations.Comment: 15 pages, 7 figure