Dynamical conductivity of AA-stacked bilayer graphene

Abstract

We calculate the dynamical conductivity of AA-stacked bilayer graphene as a function of frequency and in the presence of a finite chemical potential due to charging. Unlike the monolayer, we find a Drude absorption at charge neutrality in addition to an interband absorption with onset of twice the interlayer hopping energy. At finite doping, the interband absorption exhibits two edges which depend on both chemical potential and interlayer hopping energy. We study the behaviour as a function of varying chemical potential relative to the interlayer hopping energy scale and compute the partial optical sum. The results are contrasted with the previously published case of ABstacking. While we focus on in-plane conductivity, we also provide the perpendicular conductivity for both AB and AA stacking. We also examine conductivity for other variations with AA-stacking, such as AAA-stacked trilayer. Based on proposed models for topological insulators discussed in the literature, we also consider the effect of spin orbit coupling on the optical properties of an AA-stacked bilayer which illustrates the effect of an energy gap opening at points in the band structure.

Structure of graphene and its disorders: a review

“…(e) Low energy dispersion and (f) low energy DOS for a bilayer graphene with AA stacking. (g) Low-energy dispersion and (h) low-energy DOS for a bilayer graphene with AB stacking [157] (reused with permissions from [166] © 2016 Elsevier B.V., and [157] Copyright © 2012 American Physical Society. ). …”

“…The single spin Hamiltonians for AA-stacked and AB-stacked bilayer graphene and their corresponding matrix representations are given in Refs [157,158]. By calculation of the eigenvalues of these two matrices, the band structures of two types of bilayer are obtained and the corresponding low-energy parts are plotted in Figure 9(e,g).…”

“…Analytic expressions for the total double spin DOS of two bilayers are derived from the sum of two Dirac cone DOS which are shifted relative to each other by , and two plots of low-energy DOS are then compared in Figure 9(f,h). Because of the differences in electronic structure, AA-stacked and AB-stacked bilayers exhibit different optical conductivity [157] and responses to an external electric field [159]. The energy gap of bilayer graphene can be artificially opened by application of a perpendicular electric field [160], hence a controlled induction of an insulating state in bilayer graphene can be realized by using a dual-gate device [161].…”

“…Moreover, the formation of closed edges between adjacent graphene layers results in that AA stacking is more frequently seen in bilayer graphene so that the local strains can be reduced [164]. Further, extensive theoretical and experimental studies have been carried out to explore the properties of AA-stacked [157,164–166] and Bernal-stacked [139,158,167,168] bilayer graphenes.…”

Silicene beyond mono-layers—different stacking configurations and their properties

“…This is due to fact that silicon favors sp 3 hybridization. In the literature, there have been many theoretical and experimental studies on bi-and multi-layers of graphene in the recent past [29][30][31][32][33][34][35][36][37][38][39] . The studies on bi-layer of graphene indicate that it possesses parabolic dispersion around the highly symmetric k-point (K) in the reciprocal lattice as opposed to the linear dispersion in the case of mono-layer.…”