Raman spectra of twisted bilayer graphene close to the magic angle

Abstract

In this work, we study the Raman spectra of twisted bilayer graphene samples as a function of their twist-angles (θ), ranging from 0.03º to 3.40º, where local θ are determined by analysis of their associated moiré superlattices, as imaged by scanning microwave impedance microscopy. Three standard excitation laser lines are used (457, 532, and 633 nm wavelengths), and the main Raman active graphene bands (G and 2D) are considered. Our results reveal that electron-phonon interaction influences the G band's linewidth close to the magic angle regardless of laser excitation wavelength. Also, the 2D band lineshape in the θ < 1º regime is dictated by crystal lattice and depends on both the Bernal (AB and BA) stacking bilayer graphene and strain soliton regions (SP) [1]. We propose a geometrical model to explain the 2D lineshape variations, and from it, we estimate the SP width when moving towards the magic angle.

Electronic properties of twisted multilayer graphene

“…Calculations using continuum models [16,53] have additionally predicted a discrete series of other magic angles <1.1 • . However, in agreement with the existing experiments (most clearly, see recent articles [21,23]), atomistic calculations have demonstrated in [63] and as discussed in section 3 that these small magic angles can not be practically obtained in reconstructed TBLGs. This is essentially due to the fact that while it gets maximum at θ ≃ 1.1 • , the global electronic localization is progressively reduced, according to the increasing contribution of AB/BA stacking regions when reducing θ below <1.1 • as seen in figure 4 and more visibly in the left-panel of figure 14.…”

“…where w and t stand for interlayer and intralayer tunneling strengths, respectively. Indeed, θ MA ≈ 1.1 • is obtained, in very good agreement with experiments [21,23,24,26], with w = 0.109 eV and t = 2.7 eV. Calculations using continuum models [16,53] have additionally predicted a discrete series of other magic angles <1.1 • .…”

“…a 0 = 0.1439 nm, d 0 = 0.33 nm, r c = 0.614 nm, λ c = 0.0265 nm Indeed, such an adjusted TB Hamiltonian fairly accurately reproduces the electronic properties of TBLG as obtained in [63] as well as in experiments, e.g. in [21,23,24]. As a clear illustration, the almost flat bands near the Fermi level is perfectly reproduced in the relaxed TBLG in the vicinity of the magic angle (i.e.…”

“…In particular, and most remarkably, electronic properties of TBLG can be tuned by varying the twist angle θ [14,15], especially leading to the observation of localized flat bands near the Fermi level at a critical angle (≃1.1 • ) called 'the magic angle' [16,17]. At this critical angle, many-body effects are therefore significantly enlarged [18][19][20][21][22][23] and charge carriers do not possess enough kinetic energy to escape from their strong mutual interactions, thus forming novel strongly correlated electronic states. Such a strong electronic correlation in magic-angle TBLG is the key ingredient for observing several novel phenomena such as superconductivity, correlated insulating states, magnetism, and even quantized anomalous Hall effects [24][25][26][27][28][29][30][31][32][33].…”

Electron–Phonon Coupling in a Magic-Angle Twisted-Bilayer Graphene Device from Gate-Dependent Raman Spectroscopy and Atomistic Modeling

“…We fit the G bands with a single Lorentzian to extract their characteristics, including the band line widths (full width at half-maximum, fwhm, Γ G ) values, reported here after correction to account for the spectrometer resolution. By carrying out Raman mapping, we estimate contributions from inhomogeneity to the experimental Γ G data to be smaller than 3 cm –1 (see refs , , and and the Supporting Information for further details, including the 2D peak, also named G′ in the literature, which is not addressed here, and the D-peak range showing the absence of defects in the sample).…”