  Photonic topological insulators (PTIs) exhibit robust photonic edge states
protected by band topology, similar to electronic edge states in topological
band insulators. Standard band theory does not apply to amorphous phases of
matter, which are formed by non-crystalline lattices with no long-range
positional order but only short-range order. Among other interesting
properties, amorphous media exhibit transitions between glassy and liquid
phases, accompanied by dramatic changes in short-range order. Here, we
experimentally investigate amorphous variants of a Chern-number-based PTI. By
tuning the disorder strength in the lattice, we demonstrate that photonic
topological edge states can persist into the amorphous regime, prior to the
glass-to-liquid transition. After the transition to a liquid-like lattice
configuration, the signatures of topological edge states disappear. This
interplay between topology and short-range order in amorphous lattices paves
the way for new classes of non-crystalline topological photonic materials.
