Field theoretic study of electron-electron interaction effects in Dirac liquids

Understand

The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like systems, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems (for their Dirac composite fermions).

• These liquids are characterized by gapless bands, strong electron-electron interactions and emergent Lorentz invariance deep in the infra-red.
• We address a number of important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) as well as high-energy (particle) physics.
• We shall consider in particular the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation.