  Quantum Hall systems host chiral edge states extending along the
one-dimensional boundary of any two-dimensional sample. In solid state
materials, the edge states serve as perfectly robust transport channels that
produce a quantised Hall conductance; due to their chirality, and the
topological protection by the Chern number of the bulk bandstructure, they
cannot be spatially localized by defects or disorder. Here, we show
experimentally that the chiral edge states of a lossy quantum Hall system can
be localized. In a gyromagnetic photonic crystal exhibiting the quantum Hall
topological phase, an appropriately structured loss configuration imparts the
edge states' complex energy spectrum with a feature known as point-gap winding.
This intrinsically non-Hermitian topological invariant is distinct from the
Chern number invariant of the bulk (which remains intact) and induces mode
localization via the "non-Hermitian skin effect". The interplay of the two
topological phenomena - the Chern number and point-gap winding - gives rise to
a non-Hermitian generalisation of the paradigmatic Chern-type bulk-boundary
correspondence principle. Compared to previous realisations of the
non-Hermitian skin effect, the skin modes in this system have superior
robustness against local defects and disorders.
