Plasmon in Nonsymmorphic Dirac semimetals

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.