Geometrical and topological aspects of graphene and related materials

TL;DR

This paper reviews the geometrical and topological properties of graphene and related materials, highlighting their connections to quantum field theory, topological insulators, and recent experimental findings.

Contribution

It provides an integrated overview of the topological and geometrical aspects of graphene, linking condensed matter physics with high-energy theories and recent experimental validations.

Findings

Experimental confirmation of theoretical predictions in electronic interactions.

Analysis of spontaneous chiral symmetry breaking in model materials.

Description of topological features relevant to topological insulators.

Abstract

Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low and high-energy physics. The field has evolved very fast and very good reviews are already available in the literature. Graphene constitutes a condensed matter realization of lower dimensional quantum field theory models that were proposed to confront important -- still unresolved -- puzzles of the area: Chiral symmetry breaking and quark confinement. The new materials named topological insulators, closely related to graphene, are physical realizations of topological field theory. This article reviews some of these topics with the aim of bridging the gap and making these condensed matter issues accessible to high energy readers. The electronic interactions in the monolayer are analyzed with special emphasis on the recent experimental confirmation of some theoretical predictions. The issue of spontaneous chiral symmetry breaking in the model materials is also reviewed. Finally we give an extensive description of some recent topological aspects of graphene that allow to understand the main aspects of topological insulators.