Eur. Phys. J. B (2017) 90: 75
https://doi.org/10.1140/epjb/e2017-70664-0

Regular Article

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

¹ Laboratoire de Spectroscopie Atomique Moléculaire et Applications, Département de Physique, Faculté des Sciences de Tunis, Université Tunis El Manar, Campus Universitaire, 1060 Tunis, Tunisia
² Laboratoire de Physique de la matière condensée, Département de Physique, Faculté des Sciences de Tunis, Université Tunis El Manar, Campus Universitaire, 1060 Tunis, Tunisia
³ Université Grenoble Alpes, Inst NEEL, 38042 Grenoble, France
⁴ CNRS, Inst NEEL, 38042 Grenoble, France
⁵ Laboratoire de Physique théorique et Modélisation, CNRS and Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France

^a e-mail: guy.trambly@u-cergy.fr

Received: 8 November 2016
Received in final form: 26 January 2017
Published online: 26 April 2017

Abstract

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path L_e, the localization length ξ and the inelastic mean free path L_i. Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature T. In BLG an additional characteristic distance l₁ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1%–2%, one has l₁ ≤ L_e ≪ ξ and the BLG has transport properties that differ from those of the MLG independently of L_i(T). Whereas for larger concentration of defects L_e<l₁ ≪ ξ, and depending on L_i(T), the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.