  The Fano resonance is a widespread wave scattering phenomenon associated with
a peculiar asymmetric and ultra-sharp line shape, which has found applications
in a large variety of prominent optical devices. While its substantial
sensitivity to geometrical and environmental changes makes it the cornerstone
of efficient sensors, it also renders the practical realization of Fano-based
systems extremely challenging. Here, we introduce the concept of topological
Fano resonance, whose ultra-sharp asymmetric line shape is guaranteed by design
and protected against geometrical imperfections, yet remaining sensitive to
external parameters. We report the experimental observation of such resonances
in an acoustic system, and demonstrate their inherent robustness to geometrical
disorder. Such topologically-protected Fano resonances, which can also be found
in microwave, optical and plasmonic systems, open up exciting frontiers for the
generation of various reliable wave-based devices including low-threshold
lasers, perfect absorbers, ultrafast switches or modulators, and highly
accurate interferometers, by circumventing the performance degradations caused
by inadvertent fabrication flaws.
