Resumen de Topology and interaction effects in diran quasiparticicle systems

Adolfo Gonzalez Grushin

• In this thesis we provide ways to understand and efficiently describe the physical consequences of electron-electron interactions and topology in Dirac quasiparticle systems. We study graphene and topological insulators to understand how Dirac quasiparticles in these materials behave under different circumstances. The thesis is divided into three main parts.

  In the first part we study interaction effects in Dirac quasiparticle systems and how they affect observables. First, a phenomenological theory is constructed to recover features seen in the experimentally measured optical conductivity in graphene. Then, within diagrammatic perturbation theory, a microscopic, cut-off independent theory is constructed for Dirac quasiparticles in graphene from which observables can be calculated in a systematic way.

  In the second part, we will study how topological phases, both in their integral and fractional versions can emerge out of short range interactions in Dirac quasiparticle systems.

  First, under a mean field approach we will show that novel topological phases that break translational invariance and time reversal symmetry can appear near commensurate fillings in the honeycomb lattice. These novel phases are characterized by a finite Hall conductivity and topologically non trivial bands with Chern numbers different from zero. Then, we will present a model of Dirac quasiparticles that realizes fractional Hall effect phases. It is argued that high Chern numbers and dispersive bands can stabilize these fractional states, contrary to naive expectation based on the Landau level paradigm.

  In the final part of this thesis we will study different aspects of topological phases as well as novel physical phenomena that they can originate. We first provide a unified view of time reversal invariant topological phases appearing in graphene and its bilayer from an effective action approach. We then present two examples of topological phenomena that arise solely due to the fact that these materials are described by topological terms. On the one hand, the Casimir force between two topological insulator plates is proven to be repulsive at short distances and attractive at long distances, including the effects of finite temperature and uniaxial anisotropy. This will motivate the study of the finite frequency dependency of the topological term, which can strongly affect the Casimir effect and other topological phenomena.

  To conclude, a consistent response theory for an heterostructure of alternating ordinary and topological insulator, a Weyl semi-metal, is developed. It is shown that the effective theory of this response is a condensed matter realization of one of the possible extensions of the standard model of particle physics (Lorentz violating QED) with measurable physical consequences such as birefringence.