Van Hove Singularities and Excitonic Effects in the Optical Conductivity of Twisted Bilayer Graphene

Abstract

Abstract:We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2 eV to 5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands, as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations is essential to reproduce the shape of the conductivity spectra, and we find evidence of coherent interactions between the states associated with the multiple vHSs in tBLG.Keywords: graphene, twisted bilayer graphene, optical spectroscopy, GW-BSE In two-dimensional materials with van der Waals interlayer coupling, the rotation angle (θ) between layers has emerged as an important degree of freedom with significant effects on these materials' electronic and optical properties. Twisted bilayer graphene (tBLG), a prototypical bilayer system, has been the subject of many recent theoretical and experimental studies [1][2][3][4][5][6] . In tBLG, the interlayer interactions perturb the band structure of each graphene layer to create new, θ-dependent van Hove singularities (vHSs), which have been observed by scanning tunneling spectroscopy 5,7,8 and optical spectroscopy [9][10][11][12][13][14] . However, these previous studies focused on relatively low energies where single layer graphene (SLG) has a unique linear band structure. On the contrary, the band structure of SLG becomes more complex at higher energies: the bands lose their linearity, electrons and holes are no longer symmetric, and a saddle point vHS occurs at the M point in the SLG Brillouin zone 15,16 . To date, little is known about how this asymmetry and nonlinearity affects the θ-dependent vHSs and associated optical properties in tBLG.In addition, while it is known that there are resonant excitons associated with the M point vHS in SLG [17][18][19] , the excitonic effects associated with the interlayer vHSs in tBLG are poorly understood. Furthermore, new excitonic states could form as coherent combinations of the multiple intralayer and interlayer vHSs in tBLG, particularly those closest in energy. Understanding these effects in tBLG would also aid our understanding of other stacked and twisted two-dimensional materials, such as hexagonal boron nitride and transition metal dichalcogenides, whose single layers have intrinsic band gaps and other higher energy vHSs.In this work, we perform optical absorption spectroscopy of tBLG with known θ to explore the tBLG band structure and many-body states. For the first time, we present the full optical absorption spectra of tBLG with various θ over a large energy range (1.2 -5.6 eV), which encompasses multiple θ-dependent vHSs in tBLG as well as the absorption peak associated with the M point vHS in SLG. We find that the

Many‐body effects in optical response of graphene‐based structures

“…[92] Accounting of the excitonic effect lowered the energy of the peaks by $0.2 eV and redistributed their intensities (Fig. 10c).…”

Optical Phonons in Twisted Bilayer Graphene with Gate-Induced Asymmetric Doping

“…22 Several new Raman bands, such as R, R' and ZO' H , are activated by superlattice-induced wavevector. [25][26][27][29][30] These characteristic Raman features related to the lowenergy VHSs and superlattice atomic structure have been observed only in tBLG, [19][20][21][22][23][24][25][26][27][28][29][30][31] but not in SLG or Bernal-stacked bilayer graphene (AB-BLG).…”

“…[16][17][18] Optical spectroscopy has been exploited to study the optical and vibrational properties associated with the low-energy VHSs of tBLG. [19][20][21][22][23][24][25][26][27] These studies have demonstrated that tBLG is a prototype system to explore the influence of interlayer interaction in 2D layered materials. …”

Determination of a refractive index and an extinction coefficient of standard production of CVD-graphene

“…8,9 The optical behaviour of twisted bilayer graphene has been studied by Raman spectroscopy 10 and optical conductivity measurements. 11 Recently, graphene optical properties have found an application in photonic materials, 12 and differential transmission spectra have been used to explore the electronacoustic phonon coupling. 13 It is thus crucial for the inclusion of graphene at an industrial optoelectronic level that its transparency and optical behaviour are well understood.…”