We discuss the significance of the screening tensor of a two-dimensional material (e.g. graphene) that is either suspended or surrounded by a non-dispersive medium. This quantity, which is defined as the ratio of the applied electrical field and the total field (which includes the material's response), determines the screening of space and time dependent fields. By solving the Maxwell equations, we are able to determine the relation between the components of such a tensor and those of the space and time dependent conductivity. We also review the question of the relation between the conductivity tensor and the response functions obtained from linear response. The RPA approximation is also reviewed is such a context. Finally, a simple application of such results is discussed.

Jaime E. Santos is a post-doctoral research fellow at the Centre of Physics of the University of Minho. Most recently, he was an invited researcher at the DTU Nanotech, during 2015, and before that he was a Assistant Research Professor at the University of Minho from 2012-2014. He has also been a visitor to the Max Planck Institute for the Physics of Complex Systems and the Max Planck Institute for the Chemical Physics of Solids, both in Dresden. He was also a post-doc at the HMI in Berlin and at the TUM in Munich.