  We study the collective charge-density modes (plasmons) of two-dimensional
nonsymmorphic Dirac semimetals, within the random-phase approximation (RPA) in
presence of Coulomb interaction. Without loss of generality, we consider a
system in a two-dimensional square-lattice, based on the model originally
predicted by Young and Kane (https://doi.org/10.1103/PhysRevLett.115.126803),
where the non-interacting band-structure consists of three band-touching
points, near which the electronic states follow Dirac equations. Two of these
Dirac nodes, at the momentum points $X_1$ and $X_2$, are anisotropic, i.e.,
disperse with different velocities in different directions, whereas the third
Dirac point at $M$ is isotropic. Interestingly we find that the system of these
three Dirac nodes hold a single low-energy plasmon mode, within its
particle-hole gap, that disperses in isotropic manner, in the case when the
nodes at $X_1$ and $X_2$ are related by symmetry, which we further show in a
long-wavelength approximation. We also discuss the effects of possible
perturbations that can give rise to anisotropic plasmon dispersions. Our
results suggest, in similarity with graphene, plasmon modes of such
non-symmorphic semimetals are highly tunable and hold promise for possible
applications.
