Quantum phase transitions and critical phenomena in graphene

• Applicant: Dr. Lukas Janssen
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 230831376

Graphene defines the prototype of a substantially new class of materials, which allow to investigate the intriguing physics of relativistic fermions in table-top experiments. Previously, a significant progress in the understanding of graphene's electronic properties has been made by treating the excitations as noninteracting particles. However, recent experiments suggest that this approximation may be inadequate in a number of situations and that interactions between electrons in graphene might play a substantial role. For strong enough interactions, a transition to a Mott insulating phase is expected, mimicking the spontaneous breakdown of chiral symmetry in particle physics. In this sense, the graphene system can serve as a useful testing ground to explore the physics of strongly-correlated fermions: graphene allows to trial and improve novel field-theoretical approaches, and to compare them with the measurements. The project aims at a thorough understanding and quantitative description of quantum phase transitions in graphene with the help of modern renormalization group methods, such as the functional renormalization group. Based on a systematic classification of short-range interactions with respect to their symmetries, a low-energy effective field theory for graphene will be derived. Particular attention will be paid to the effect of the long-range tail of Coulomb interaction. In a second step, the partial bosonization technique will allow to quantitatively describe the critical behavior of the system in the vicinity of the phase transition. The third part of the project focuses on an analysis of insulating phases in graphene and related systems in different dimensions. In particular, excitations with nontrivial topology will be considered, which might play a decisive part for the phase transition.

• DFG Programme: Research Fellowships
• International Connection: Canada
• Host: Professor Dr. Igor Herbut