Plasmons and dynamic screening effects in crystals

Abstract Plasmon energies are closely related to the complex zeros of the determinant of the dielectric matrix or, equivalently, to the complex poles of the dynamically screened interaction matrix of electronic systems. In this paper we first clarify the true positions of these zeros, or poles, in the complex energy plane. Concluding that these points are on the non-physical Riemann sheets associated with the above-mentioned matrices, we present two methods which enable us to determine not only the plasmon energy bands but also their lifetimes throughout the whole Brillouin zone. We present, among other things, the plasmon energy bands of silicon in the diamond structure (within the norm-conserving pseudopotential framework) along a symmetry axis. Finally, we demonstrate how the electronic self-energy operator within the Hedin GW framework can be accurately and relatively easily calculated.