Electronic Properties and Hidden Symmetries of Graphene

TL;DR

This paper explores the hidden SU(3) symmetry in graphene's structure and electronic properties, revealing how electronic momentum conservation and wave phases relate to SU(3) representations and classifications.

Contribution

It uncovers the SU(3) symmetry underlying graphene's electronic structure and links it to momentum conservation and wave phase quantization.

Findings

Electronic momenta conservation is described by SU(3) representations.

Fourier wave functions classified by SU(3) highest weight multiplets.

Wave phase angles are quantized based on SU(3) parameters.

Abstract

Using the relation between the structural and the electronic properties of honeycomb, we study the hidden SU(3) symmetry of the graphene monolayer and exhibit the link with its electronic properties. We show that the conservation law of incoming and outgoing electronic momenta at each site of graphene is solved in terms of SU(3) representations; and the Fourier waves {\phi}(k_{x},k_{y}) of the hopping electron may be classified by SU(3) highest weight multiplets {\phi}_{p,q}({\xi}). It is also shown that the phases arctan((k_{y})/(k_{x})) of the waves are quantized as (((p+q))/((p-q)))sqrt(3) with p, q positive integers. Other features are also discussed.