Electronic properties and the quantum Hall effect in bilayer graphene

Abstract

In this paper, I review the quantum Hall effect (QHE) and far-infra red (FIR) absorption properties of bilayer graphene in a strong magnetic field. This includes a derivation of the effective low-energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: the form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model groundstates of the bilayer QHE system based on the different absorption characteristics of right-and left-handed polarization of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture.

Evolution of Graphene Growth on Ni and Cu by Carbon Isotope Labeling

“…The data presented in this paper on graphene growth on Cu substrates clearly marks a path to monolayer graphite growth on Cu and perhaps also on other substrate materials where carbon solubility is low and precipitation is not observed. However, if one wants to grow controlled bi-layer graphene which has been found to show some desirable electronic properties, then a precipitation process will have to be taken advantage of in conjunction with solubility 28 . Since Cu and Ni are miscible, one can envision a Cu-Ni alloy with appropriate composition to tune the solubility of C in the alloy 29 and hence enable bilayer graphene growth (or trilayer, etc.).…”

Ultra-Quantum 2D Materials: Graphene, Bilayer Graphene, and Other Hall Systems—New Non-Local Quantum Theory of Hall Physics

“…Before we proceed to the main aim of this section, it is worth discussing differences in the Landau level ladder between conventional 2DEG, monolayer and bilayer graphene samples (as well as their possible consequences). We first note that in both graphene structures, LLs are not distributed equidistantly on the energy axis, which was the case for typical quantum wells [36][37][38][39]. However, the latter is not reflected in the topological approach-an area encircled by a single-loop cyclotron orbit (A) is proportional to the bare kinetic energy of electrons (E k ) and not the general energy determined by LLs.…”

“…The unparalleled basic set of fillings -with ν = 1 / 2 being the most robust incompressible state -has its origin in the appearance of an additional surface [28,55]. The supplementary sheet of carbon atoms, coupled to the primary one by a nonzero hopping integral [36][37][38][39], leads to the electron density located in both graphene planes. As a result, bilayer graphene samples are not strictly two-dimensional.…”

Electrostatic Deposition of Large-Surface Graphene

“…A decade ago, graphene exfoliation from bulk graphite by repeated surface cleaving using household Scotch tape was changing the world we live-in [ 1 , 2 , 3 , 4 ]. Since then, massive worldwide efforts explored the unique physical properties of single-and few-layer grapheme [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], including its optical [ 10 , 13 , 14 , 15 , 16 , 17 ] and electrical [ 5 , 6 , 10 , 13 , 15 , 16 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ] properties. Novel deposition methods have also generated significant interest due to growing demands for large-scale device integration.…”