Relativistic energy-momentum transfer and electromagnetic conservation laws in the interaction of moving charged particles with two-dimensional materials

We explore the conservation of energy and momentum by solving Maxwell's equations for a charged particle passing through a single conductive sheet. By using a fully relativistic formulation of the problem, we evaluate the energy and momentum transfer from charged particle to electronic excitations localized in the sheet and to electromagnetic radiation emitted from the sheet in the far-field region. Using a suitable conductivity model for the sheet that can represent graphene or other two-dimensional (2D) material, our theory can elucidate the energy and momentum transfer involving the incident particle, plasmon polariton mode(s) in the 2D material, and the induced transition radiation from it.