Theoretical seminar | 14 July 2021

In this presentation, I first give a short overview of a homogenization theory able to describe in terms of a few effective parameters the propagation of light waves in periodic metamaterials as well as of electron waves in bulk semiconductor or superlattices. In the second part of the talk, I apply this theory to the homogenization of an instance of artificial graphene made of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry. It is shown that the band structure obtained from a two components effective medium Hamiltonian is exactly coincident with what is found from the microscopic Hamiltonian. In addition, it is demonstrated that near the K-point the dynamics of such two-dimensional electron gas is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer. Finally, it is emphasized that the same homogenization scheme applies to a photonic instance of artificial graphene made of a photonic crystal with a metallic background.

Main paper/arXiv, related to the seminar, and other references

1. http://dx.doi.org/10.1103/PhysRevB.91.045416

2. https://doi.org/10.5802/crphys.4

3. https://doi.org/10.1515/nanoph-2019-0037