Quantum field theory in Dirac materials

Abstract

A good part of the progress achieved in condensed matter physics over the recent years is related to the so called Dirac materiais. In these materiais, the quasiparticles obey the Dirac equation. Graphene, topological insulators and Weyl semimetals are the most prominent examples of this c1ass. Quantum Field Theory (QFT) is a natural instrument to study the properties of these materiais. In this project we shall address some geometrical aspects of QFT in the Dirac materiais. In particular, we shall study the parity anomaly for Dirac operator in the presence of boundaries and the induced Chern-Simons actions. We shall apply QFT to compute the Casimir interaction of graphene nanoribbons with anisotropic materiais (strained graphene, e.g.). Besides, we propose to attack the subtleties of Quantum Hall Effect in these materiais forming genus one Riemann surfaces through using the Riemannian Theta Function Theory.We shall study the Kosterlitz-Thouless phase transitions which requires the addition of scalar fields in non-linear sigma models. Topological defects of kink type in linear spin chains or vortexesin planar gauged sigma models, with either Maxwell or Chern-Simons fields, playa crucial role. (AU)