  We theoretically study a topological nanospaser, which consists of a silver
nanospheroid and MoS$_2$ monolayer ake of a circular shape. The metal
nanospheroid acts as a plasmonic nanoresonator that supports two rotating
modes, which are coupled to the corresponding valleys of MoS$_2$. We apply
external circularly polarized light that selectively pumps only one of the
valleys of MoS$_2$. The generated spaser dynamics strongly depends on the size
(radius) of the MoS$_2$ nanoflake. For small radius, the system has only one
spasing regime when only chirally-matched plasmon mode is generated, while at
larger size of MoS$_2$, depending on the pump intensity, there are two regimes.
In one regime, only the chirally-matched plasmon mode is generated, while in
the other regime both chirally-matched and chirally-mismatched modes exist.
Different regimes of spaser operation have also opposite handedness of the
far-field radiated of the spaser system. Such topological nanospaser has
potential applications in different areas of infrared spectroscopy, sensing,
probing, and biomedical treatment.
