Electronic Properties of Disordered Two-Dimensional Carbon

TL;DR

This paper investigates how various types of defects affect the electronic, magnetic, and transport properties of graphene, revealing universal conductance, defect-induced states, and potential magnetic phenomena.

Contribution

It provides a comprehensive self-consistent analysis of both localized and extended defects on graphene's electronic and transport properties, including effects on conductivity, magnetism, and quantum Hall phenomena.

Findings

Localized defects cause a finite elastic lifetime and enhance density of states near the Fermi level.

Disorder leads to a universal, temperature-independent conductivity at low temperatures.

Extended defects induce localized states and self-doping effects.

Abstract

Two-dimensional carbon, or graphene, is a semi-metal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene. On the one hand, point defects induce a finite elastic lifetime at low energies with the enhancement of the electronic density of states close to the Fermi level. Localized disorder leads to a universal, disorder independent, electrical conductivity at low temperatures, of the order of the quantum of conductance. The static conductivity increases with temperature and shows oscillations in the presence of a magnetic field. The graphene magnetic susceptibility is temperature dependent (unlike an ordinary metal) and also increases with the amount of defects. Optical transport properties are also calculated in detail. On the other hand, extended defects induce localized states near the Fermi level. In the absence of electron-hole symmetry, these states lead to a transfer of charge between the defects and the bulk, the phenomenon we call self-doping. The role of electron-electron interactions in controlling self-doping is also analyzed. We also discuss the integer and fractional quantum Hall effect in graphene, the role played by the edge states induced by a magnetic field, and their relation to the almost field independent surface states induced at boundaries. The possibility of magnetism in graphene, in the presence of short-range electron-electron interactions and disorder is also analyzed.