Topological insulators (TIs) present a neoteric class of materials, which
support delocalised, conducting surface states despite an insulating bulk. Due
to their intriguing electronic properties, their optical properties have
received relatively less attention. Even less well studied is their behaviour
in the nanoregime, with most studies thus far focusing on bulk samples - in
part due to the technical challenges of synthesizing TI nanostructures. We
study topological insulator nanoparticles (TINPs), for which quantum effects
dominate the behaviour of the surface states and quantum confinement results in
a discretized Dirac cone, whose energy levels can be tuned with the
nanoparticle size. The presence of these discretized energy levels in turn
leads to a new electron-mediated phonon-light coupling in the THz range. We
present the experimental realisation of Bi$_2$Te$_3$ TINPs and strong evidence
of this new quantum phenomenon, remarkably observed at room temperature. This
system can be considered a topological quantum dot, with applications to room
temperature THz quantum optics and quantum information technologies.