Electronic Transport in Graphene: Quantum Effects and Role of Local Defects

TL;DR

This paper investigates quantum transport in graphene, analyzing how local defects like vacancies affect conductivity and diffusion, and highlights the role of quantum effects such as Zitterbewegung in electronic behavior.

Contribution

It provides analytical and numerical insights into quantum diffusion and conductivity in graphene with defects, including the effects of velocity fluctuations and local vacancies.

Findings

Analytical time-dependent diffusion in pure graphene

Identification of velocity fluctuation effects (Zitterbewegung)

Dependence of diffusion and conductivity on defect concentration and energy

Abstract

In this paper we present generic properties of quantum transport in mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the square spreading of wave packets of a given energy with is directly related to conductivity. As a first result, we compute analytically the time dependent diffusion for pure graphene. In addition to the semi-classical term a second term exists that is due to matrix elements of the velocity operator between electron and hole bands. This term is related to velocity fluctuations i.e. Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in graphene with simple vacancies and pair of neighboring vacancies (divacancies), that simulate schematically oxidation, hydrogenation and other functionalisations of graphene. We analyze in particular the time dependence of the diffusion and its dependence on energy in relation with the electronic structure. We compute also the mean free path and the semi-classical value of the conductivity as a function of energy in the limit of small concentration of defects.