  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.
