Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-03-21
Modern Physics Letters B, Vol. 25, Nos. 12 & 13 (2011) 1019-1028
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
10 pages, 5 figures
Scientific paper
10.1142/S0217984911026747
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.
de Laissardiere Guy Trambly
Mayou Didier
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