Using a tight-binding Hamiltonian for phosphorene, we have calculated the real part of the polarizability and the corresponding dielectric function, Re[ ϵ q ω ], at absolute zero temperature (T = 0 K) with free carrier density 10 13 / cm 2 . We present results showing Re[ ϵ q ω ] in different directions of the transferred momentum q. When q is larger than a particular value which is twice the Fermi momentum kF, Re[ ϵ q ω ] becomes strongly dependent on the direction of q . We also discuss the case at room temperature (T = 300 K). These results which are similar to those previously reported by other authors are then employed to determine the static shielding of an impurity in the vicinity of phosphorene.
Part of the book: 2D Materials
The purpose of this chapter is to review some important, recent theoretical discoveries regarding the effect of temperature on the property of plasmons. These include their dispersion relations and Landau damping rates, and the explicit dependence of plasmon frequency on chemical potential at finite temperatures for a diverse group of recently discovered Dirac-cone materials. These novel materials cover gapped graphene, buckled howycomb lattices (such as silicene and germanene), molybdenum disulfide and other transition-metal dichalcogenides, especially the newest dice and α-T3 materials. The most crucial part of this review is a set of implicit analytical expressions about the exact chemical potential for each of considered materials, which greatly affects the plasmon dispersions and a lot of many-body quantum-statistical properties. We have also obtained the nonlocal plasmon modes of graphene which are further Coulomb-coupled to the surface of a thick conducting substrate, while the whole system is kept at a finite temperature. An especially rich physics feature is found for α-T3 materials, where each of the above-mentioned properties depends on both the hopping parameter α and temperature as well.
Part of the book: Nanoplasmonics