Infrared markers of topological phase transitions in quantum spin Hall insulators

Using first principles techniques, we show that infrared optical response allows us to discriminate between the topological and the trivial phases of 2D quantum spin Hall insulators (QSHI). We showcase germanene and jacutingaite, of recent experimental realization, as prototypical systems where the infrared spectrum is discontinuous across the transition, due to sudden and large discretized jumps of the Born effective charges (up to similar to 2). Our results, rationalized thanks to the low-energy Kane-Mele model, are robust with respect to dynamical effects, relevant when the electronic energy gap is comparable with the phonon frequency. In the small gap QSHI germanene, due to dynamical effects, the in-plane phonon resonance in the optical conductivity shows a Fano profile with remarkable differences in the intensity and the shape between different phases. Instead, the large-gap QSHI jacutingaite presents several IR-active phonon modes whose spectral intensities drastically change between different phases.