The electronic properties of graphene

TL;DR

This review paper discusses the fundamental electronic properties of graphene, emphasizing the behavior of Dirac electrons under various conditions and how stacking, edges, and disorder influence its electronic characteristics.

Contribution

It provides a comprehensive overview of the theoretical understanding of graphene's electronic properties, including effects of external fields, stacking, edges, disorder, and interactions.

Findings

Dirac electrons exhibit unusual tunneling and quantum Hall effects.

Stacking order and layer number significantly influence electronic properties.

Edge termination affects nanoribbon surface states and related properties.

Abstract

This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.