We consider the effect of the Coulomb interaction in a nonsymmorphic Dirac semimetal, leading to collective charge oscillation modes (plasmons), focusing on the model originally predicted by Young and Kane [Phys. Rev. Lett. 115, 126803 (2015)]. We model the system in a two-dimensional square-lattice and evaluate the density-density correlation function within the random-phase approximation (RPA) in presence of the Coulomb interaction. 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, disperses 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. We also show this analytically using a long-wavelength approximation. We discuss effects of perturbations that can give rise to anisotropic plasmon dispersions and comment on possible experimental observation of our prediction.
Download