Graphene conductivity near the charge neutral point

Abstract

Disordered Fermi-Dirac distributions are used to model, within a straightforward and essentially phenomenological Boltzmann equation approach, the electron/hole transport across graphene puddles. We establish, with striking experimental support, a functional relationship between the graphene minimum conductivity, the mobility in the Boltzmann regime, and the steepness of the conductivity parabolic profile usually observed through gate-voltage scanning around the charge neutral point.

Nondiagonal graphene conductivity in the presence of in-plane magnetic fields

“…In the Boltzmann equation approach, one assumes that scattering by impurities is encoded in the relaxation time approximation, while charged puddles can be modeled as extended subregions of the sample where the chemical potential is approximately uniform, but randomly fluctuating from puddle to puddle. In that way, a phenomenological relation between the minimum conductivity value, the electron/hole mobility parameter (in the semiclassical re-gion) and the steepness of the conductivity parabola around the charge neutral point has been predicted and clearly supported by an extensive compilation of experimental data [11].…”

“…We extend in this work the Boltzmann equation approach put forward in [11] to the more general context of graphene transport in the presence of in-plane magnetic fields, where, as discussed in the preceding section, surface roughness becomes an additional source of disorder. We deal, more specifically, with approximately semiclassical transport regimes characterized by a mean free path k and a surface correlation height L which are both larger than the scattering wavelength ∼ k −1 and both smaller than the typical charged puddle linear size L p , that is,…”

“…[11], with reasonable phenomenological success, that the probability distribution function (pdf) of ξ can be written as…”

“…The evaluation of (26) and (27) is performed with the help of (15) and two useful relations taken from Ref. [11], viz.,…”

“…III, we develop, following the Boltzmann equation approach of Ref. [11], a treatment of the semiclassical electron/hole transport in graphene samples disordered by the presence of charged puddles [12] and subject to in-plane magnetic fields. We, then, work out numerical estimates of the conductivity tensor components, which are noted to be perfectly within the reach of present experimental resolution.…”