Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers

TL;DR

This paper presents a unified theoretical framework for understanding the dc conductivity of monolayer and bilayer graphene at finite densities, emphasizing the role of resonant scatterers like adsorbed hydrocarbons and their impact on electronic transport properties.

Contribution

It introduces a comprehensive scattering model based on resonant impurities, establishing equivalence among different scattering approaches and analyzing conductivity behavior near the neutrality point and under bias.

Findings

Resonant impurities create impurity bands near the Dirac point.

A minimum conductivity plateau of about e^2/h per layer is observed.

In bilayer graphene, high impurity concentrations can induce an energy gap.

Abstract

We show that a coherent picture of the dc conductivity of monolayer and bilayer graphene at finite electronic densities emerges upon considering that strong short-range potentials are the main source of scattering in these two systems. The origin of the strong short-range potentials may lie in adsorbed hydrocarbons at the surface of graphene. The equivalence among results based on the partial-wave description of scattering, the Lippmann-Schwinger equation, and the T-matrix approach is established. Scattering due to resonant impurities close to the neutrality point is investigated via a numerical computation of the Kubo formula using a kernel polynomial method. We find that relevant adsorbate species originate impurity bands in monolayer and bilayer graphene close to the Dirac point. In the midgap region, a plateau of minimum conductivity of about $e^2/h$ (per layer) is induced by the resonant disorder. In bilayer graphene, a large adsorbate concentration can develop an energy gap between midgap and high-energy states. As a consequence, the conductivity plateau is supressed near the edges and a "conductivity gap" takes place. Finally, a scattering formalism for electrons in biased bilayer graphene, taking into account the degeneracy of the spectrum, is developed and the dc conductivity of that system is studied.