Twisted bilayer graphene - electronic and optical properties

03/02/2017

The study of the properties of van der Waals heterostructures is a new trending research field in condensed matter physics, with huge potential [1-3] but still in an early stage. In this thesis, we focus on the theoretical description of one of the simplest stackings, the twisted bilayer graphene, which can be seen as one of the fundamental pieces for more complex assemblies. We reproduce a single-particle theory, based on a low-energy continuum model, for the electronic states in this material; the profile determination of the density of states and the carrier density follows directly. Then, we proceed with the study of the optical properties, namely the optical conductivity (within the linear response theory) and the spectrum of graphene surface plasmon-polaritons (using a semi-classical treatment). Lastly, we address the effects of electron-electron interactions, in particular the self-energy correction term for the band renormalization due to the long range (screened) Coulomb repulsion. In this work, a profound understanding of the most recent semi-analytical effective models and their features was attained. As for the optical conductivity calculations, our results were compatible with the literature and we also discussed the numerical implementations, introducing a new and improved method for computing the Drude conductivity. Original results for the plasmonic response of this system were achieved. Regarding the electron-electron interaction effects, although we could not fulfill this gap in the literature, we believe we have provided a useful discussion on how to tackle the difficulties in future works.

Authors in the community:

• 

  G

  Gonçalo Filipe Santos Catarina

  ist172788

Supervisors of this institution:

• 

  E

  Eduardo Filipe Vieira de Castro

  ist25287

physical-sciences - Physical sciences

eng - English

Instituto Superior Técnico