Collective excitations in three-dimensional Dirac systems

We provide the plasmon spectrum and related properties of the three-dimensional (3D) Dirac semimetals Na₃Bi and Cd₃As₂ based on the random-phase approximation. The necessary one-electron eigenvalues and eigenfunctions are obtained from an effective k·p Hamiltonian. Below the energy at which the velocity vz along the kz axis vanishes, the density of states differs drastically from that of a 3D electron gas (3DEG) or graphene. The dispersion relation is anisotropic for wave vectors parallel (q) and perpendicular (qz) to the $(x,y)$ plane and is markedly different than that of graphene or a 3DEG. The same holds for the energy-loss function. Both depend sensitively on the position of the Fermi energy EF relative to the region of the Berry curvature of the bands. For EF below the energy at which vz vanishes, the range of the relevant wave vectors q and qz shrinks, for qz by about one order of magnitude.