  The bulk-boundary correspondence is a key concept in topological quantum
materials. For instance, a quantum spin Hall insulator features a bulk
insulating gap with gapless helical boundary states protected by the underlying
Z2 topology. However, the bulk-boundary dichotomy and distinction are rarely
explored in optical experiments, which can provide unique information about
topological charge carriers beyond transport and electronic spectroscopy
techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and
pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses
of Bi4Br4, a recently discovered room-temperature quantum spin Hall insulator.
Benefiting from the low energy of infrared photons and the high spatial
resolution, we unambiguously resolve a strong absorption from the boundary
states while the bulk absorption is suppressed by its insulating gap. Moreover,
the boundary absorption exhibits a strong polarization anisotropy, consistent
with the one-dimensional nature of the topological boundary states. Our
infrared pump-probe microscopy further measures a substantially increased
carrier lifetime for the boundary states, which reaches one nanosecond scale.
The nanosecond lifetime is about one to two orders longer than that of most
topological materials and can be attributed to the linear dispersion nature of
the helical boundary states. Our findings demonstrate the optical bulk-boundary
dichotomy in a topological material and provide a proof-of-principal
methodology for studying topological optoelectronics.
