  The behavior of electrons in condensed matter systems is mostly determined by
the repulsive Coulomb interaction. However, under special circumstances the
Coulomb interaction can be effectively attractive, giving rise to electron
pairing in unconventional superconductors and specifically designed mesoscopic
setups. In quantum Hall systems electron interactions can play a particularly
important role due to the huge degeneracy of Landau levels, leading for
instance to the emergence of quasi-particles with fractional charge and anyonic
statistics. Quantum Hall Fabry-P\'erot (FPI) interferometers have attracted
increasing attention due to their ability to probe such exotic physics. In
addition, such interferometers are affected by electron interactions themselves
in interesting ways. Recently, experimental evidence for electron pairing in a
quantum Hall FPI was found (H.K. Choi et al., Nat. Comm 6, 7435 (2015)) .
Theoretically describing an FPI in the limit of strong backscattering and under
the influence of a screened Coulomb interaction, we compute electron shot noise
and indeed find a two-fold enhanced Fano factor for some parameters, indicative
of electron pairing. This result is explained in terms of an electron
interaction due to exchange of neutral inter-edge plasmons, so-called
neutralons.
