Equations of macroscopic electrodynamics for two-dimensional crystals

The electrodynamics of two-dimensional (2D) dielectric and conducting layers cannot be described by such three-dimensional macroscopic quantities as the dielectric constant $ϵ$ or the refractive index $n$. By means of the proper averaging of the microscopic Maxwell equations we derive general macroscopic electrodynamic equations for 2D crystals and discuss some of their consequences.