You need to use :sup:<whatever you want in superscript>, there has to be a space before the :sup: though. To prevent this space from being printed mark it with an escape \, etc: \ :sup:<whatever you want in superscript>

The correct docstring for my case as an example would be:

:param ne_0: mean electron density
:type ne_0: float, default: 1e24 m\ :sup:`-3`