Graphene and Cousin Systems

TL;DR

This paper explores the physical properties and symmetries of graphene and related systems using tight binding, field theory, and symmetry analysis, connecting 2D graphene to lattice QCD models.

Contribution

It introduces a unified approach combining tight binding and symmetry methods to study graphene and its cousins, linking condensed matter and high-energy physics models.

Findings

Analysis of hidden symmetries in graphene and related structures

Connection between 2D graphene properties and 4D lattice QCD models

Insights into the physical and electronic features of graphene and its extensions

Abstract

Graphene is a new material that exhibits remarkable properties from both fundamental and applied issues. This is a 2D matter system whose physical and mechanical features have been approached by using tight binding model, first principle calculations based on DFT and membrane theory. Graphene as a carbon molecule has also hidden symmetries that motivated extensions in various dimensions such as chain-type configurations, that are frequently observed as the graphene bridge narrowed down to a few- or single-atom width, graphene multi-layers thought of as electric capacitors, doped graphene to gain more physical properties as well as cousin systems such as diamond and hyperdiamond. In this work, we use tight binding model ideas and field theory method as well as the hidden symmetries of the underlying crystals to study physical aspects of 2D graphene and its homologues. We also study the relation between 2D graphene with the Bori\c{c}i-Creutz fermions considered recently in literature as an adequate model to perform numerical simulations in 4D lattice QCD where the two Dirac zeros are interpreted in terms of the light quarks up and down.