Determination of the gate-tunable band gap and tight-binding parameters in bilayer graphene using infrared spectroscopy

Abstract

We present a compelling evidence for the opening of a bandgap in exfoliated bottom-gated bilayer graphene by fitting the gate-voltage-modulated infrared reflectivity spectra in a large range of doping levels with a tight-binding model and the Kubo formula. A close quantitative agreement between the experimental and calculated spectra is achieved, allowing us to determine self-consistently the full set of Slonczewski-WeissMcClure tight-binding parameters together with the gate-voltage-dependent bandgap. The doping dependence of the bandgap shows a good agreement with the existing calculations that take the effects of self-screening into account. We also identify certain mismatches between the tight-binding model and the data, which can be related to electron-electron and electron-phonon interactions.

The electronic properties of bilayer graphene

“…Thus, there are five independent parameters in the Hamiltonian (16) of intrinsic bilayer graphene, namely γ 0 , γ 1 , γ 3 , γ 4 and ∆ ′ . The band structure predicted by the tight-binding model has been compared to observations from photoemission [16], Raman [76] and infrared spectroscopy [55,56,[78][79][80][81]. Parameter values determined by fitting to experiments are listed in Table I for bulk graphite [67], for bilayer graphene by Raman [76,77] and infrared [55,56,80] spectroscopy, and for a This parameter was not determined by the given experiment, the value quoted was taken from previous literature.…”

“…The electronic structure of bilayer graphene was probed by spectroscopic measurements in zero magnetic field [16,55,56,79,80,129,130], and also in high magnetic fields [78]. The optical absorption for perpendicularly incident light is described by the dynamical conductivity in a electric field parallel to the layers, in both symmetric bilayers [164,[226][227][228] and in the presence of an interlayer-asymmetry gap [227] For symmetric bilayer graphene, this is explicitly estimated as [164,[226][227][228] Re σ xx (ω) = g v g s 16…”

“…Plots were made using Hamiltonian H b , equation (16), with parameter values determined by infrared spectroscopy γ 0 = 3.16 eV, γ 1 = 0.381 eV, γ 3 = 0.38 eV, γ 4 = 0.14 eV, ǫ B1 = ǫ A2 = ∆ ′ = 0.022 eV, and ǫ A1 = ǫ B2 = U = δ AB = 0 [80]. There are four bands because the model takes into account one 2p z orbital on each of the four atomic sites in the unit cell; a pair of conduction bands and a pair of valence bands.…”

Landau level spectra and the quantum Hall effect of multilayer graphene

“…21,22,28,29,32 By comparison with experiments, it has been possible to determine the values of relevant parameters, including intralayer coupling 2,3,51,52 and, in bilayers, interlayer couplings. 17,[53][54][55][56][57][58] Although it is possible to numerically diagonalize an effective Hamiltonian with 2N components, [33][34][35] this approach does not always shed light on the roles of the different parameters. Nevertheless, it was noticed that the multilayer bands form groups of bilayerlike parabolic bands near the corners of the Brillouin zone called valleys 59 with, in odd-N layers, an additional pair of monolayerlike bands with linear dispersion.…”

Localized States due to Expulsion of Resonant Impurity Levels from the Continuum in Bilayer Graphene

“…The most important property of bilayer graphene to this extent is its gap tunable by external bias [19][20][21]. It is therefore important to elucidate how strongly the gap is affected by the disorder, which generally tends to smear the gap.…”