Detecting band inversions by measuring the environment: fingerprints of electronic band topology in bulk phonon linewidths

The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases and quantum information. While recent studies suggest that dissipative baths can induce topological phases in intrinsically trivial quantum materials, the backaction of topological invariants on dissipative baths is overlooked. By exploring this backaction for a centrosymmetric Dirac insulator coupled to phonons, we show that the linewidths of bulk optical phonons can contain generic features that reveal the topology of the electronic structure. This result is the first known example where topological phases of an open quantum system may be detected by measuring the bulk properties of the surrounding environment.