  Electronic topological states of matter exhibit novel types of responses to
electromagnetic fields. The response of strong topological insulators, for
instance, is characterized by a so-called axion term in the electromagnetic
Lagrangian which is ultimately due to the presence of topological surface
states. Here we develop the axion Mie theory for the electromagnetic response
of spherical particles including arbitrary sources of fields, i.e., charge and
current distributions. We derive an axion induced mixing of transverse magnetic
and transverse electric modes which are experimentally detectable through small
induced rotations of the field vectors. Our results extend upon previous
analyses of the problem. Our main focus is on the experimentally relevant
problem of electron energy loss spectroscopy in topological insulators, a
technique that has so far not yet been used to detect the axion electromagnetic
response in these materials.
