PhD Comprehensive Exam | Milad Moshayedi, Mathematical modeling and computer simulation of interactions of charged particles with 2D materials

Tuesday, September 20, 2022 1:00 pm - 1:00 pm EDT (GMT -04:00)

MS Teams (please email for the meeting link)


Milad Moshayedi | Applied Mathematics, University of Waterloo


Mathematical modeling and computer simulation of interactions of charged particles with 2D materials


When a charged particle is moving above the flat surface of a 2-dimensional (2D) layer that might be supported with a substrate or not, energy dissipation occurs. This energy dissipation takes place through the electromagnetic forces which act on the moving particle as the response of the target material to that moving charge. Therefore, these forces and their energy dissipation can provide valuable information on the nature of the target material. In this study, we consider the typical settings for high-resolution electron energy loss spectroscopy (HREELS) which is a well-known technique to characterize the surface response of different materials, to develop a formulation that makes a connection between the electromagnetic forces (which are observable) and material properties of the target system. To achieve this goal, we used a dielectric response theory to describe electrodynamic forces on a charged particle moving parallel to a supported 2D layer, in non-retarded regime. 2D materials could be either isotropic or anisotropic, and in each case, an appropriate model for the in-plane conductivity tensor must be considered. In this study, the calculations of the forces are performed for the Graphene which is isotropic, and for the Phosphorene which is anisotropic. In each case, we assumed that the 2D layer is supported by an isotropic supporting material, and relevant models for the effective dielectric function of the system in the THz-MIR range of frequencies are developed. It is shown that the stopping forces could be described in terms of the energy loss function (ELF) of the target materials, and in the case of Phosphorene, the stopping force can have a transverse component that is perpendicular to the particle's trajectory and its magnitude is comparable to that of the longitudinal stopping force. Moreover, In the case of Graphene, using a Kramers–Kronig relation, the conservative image force is expressed in terms of the ELF of the target material which encompasses all the energy loss channels in the target. Finally, dispersion relations of the surface plasmon modes (for the free standing 2D materials) and hybrid plasmon-phonon modes (for the supported 2D materials), and the dependency of the electromagnetic forces on the experimental parameters like the speed of the particle, its distance from the layer, and its direction with respect to the target in the case of Phosphorene are investigated.