Experimental characterization of spectral flow between fragile bands.
Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, posses crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. While an intriguing concept by itself, there was no known direct experimental consequence of fragile topology. Here, we present an unambiguous spectral signature of fragility in an acoustic crystal in the form of spectral flow under twisted boundary conditions. Additionally, we fully characterize the symmetry properties of the measured acoustic response to firmly establish the fragile nature of the low-lying Bloch bands.