Dirac plasmon polaritons and magnetic modes in topological-insulator nanoparticles

We demonstrate the existence of previously unreported magnetic modes with record-high magnetic Purcell factors in topological-insulator nanospheres. Focusing on bismuth selenide (Bi$_{2}$Se$_{3}$), and based on full electromagnetic Mie theory, we find magnetic modes arising from both displacement current loops in the bulk, and surface currents due to delocalized surface states, induced by electronic transitions between topologically protected states within the Dirac cone and discretized due to the sphere finite size. Furthermore, we discuss how Dirac plasmon polaritons, resulting from the interaction between THz photons and Dirac electrons, dramatically influence both the magnetic and the electric transitions of quantum emitters placed near Bi$_2$Se$_3$ nanospheres, significantly enhancing the corresponding Purcell factors. These findings position Bi$_{2}$Se$_{3}$ nanospheres, whose optical response is related to a richness of physical mechanisms, among the most promising candidates for enhancing light--matter interactions in nanophotonics and THz technologies.