  Extensive efforts have been undertaken to combine superconductivity and the
quantum Hall effect so that Cooper-pair transport between superconducting
electrodes in Josephson junctions is mediated by one-dimensional edge states.
This interest has been motivated by prospects of finding new physics, including
topologically-protected quasiparticles, but also extends into metrology and
device applications. So far it has proven challenging to achieve detectable
supercurrents through quantum Hall conductors. Here we show that domain walls
in minimally twisted bilayer graphene support exceptionally robust proximity
superconductivity in the quantum Hall regime, allowing Josephson junctions to
operate in fields close to the upper critical field of superconducting
electrodes. The critical current is found to be non-oscillatory and practically
unchanging over the entire range of quantizing fields, with its value being
limited by the quantum conductance of ballistic, strictly one-dimensional
electronic channels residing within the domain walls. The system described is
unique in its ability to support Andreev bound states at quantizing fields and
offers many interesting directions for further exploration.
