In this paper, the electronic properties of 30° twisted double bilayer graphene, which loses the translational symmetry due to the incommensurate twist angle, are studied by means of the tight-binding approximation. We demonstrate the interlayer decoupling in the low-energy region from various electronic properties, such as the density of states, effective band structure, optical conductivity and Landau level spectrum. However, at Q points, the interlayer coupling results in the appearance of new Van Hove singularities in the density of states, new peaks in the optical conductivity and importantly the 12-fold-symmetry-like electronic states. The k-space tight-binding method is adopted to explain this phenomenon. The electronic states at Q points show the charge distribution patterns more complex than the 30° twisted bilayer graphene due to the symmetry decrease. These phenomena appear also in the 30° twisted interface between graphene monolayer and AB stacked bilayer.
Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHS…
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
We have studied the phonon specific heat in single-layer, bilayer and twisted bilayer graphene. The calculations were performed using the Born-von Karman model of lattice dynamics for intralayer atomic interactions and spherically symmetric interatomic potential for interlayer interactions. We found that at temperature T<15 K, specific heat varies with temperature as T^n, where n = 1 for graphene, n = 1.6 for bilayer graphene and n = 1.3 for the twisted bilayer graphene. The phonon specific heat reveals an intriguing dependence on the twist angle in bilayer graphene, which is particularly pron…
The discovery of electric field induced bandgap opening in bilayer graphene opens new door for making semiconducting graphene without aggressive size scaling or using expensive substrates. However, bilayer graphene samples have been limited to um size scale thus far, and synthesis of wafer scale bilayer graphene posts tremendous challenge. Here we report homogeneous bilayer graphene films over at least 2 inch x 2 inch area, synthesized by chemical vapor deposition on copper foil and subsequently transferred to arbitrary substrates. The bilayer nature of graphene film is verified by Raman spect…
Using first-principles calculations, we study the structural and electronic properties of the bilayer SnS/graphene, bilayer SnS/bilayer graphene (AA-stacked), bilayer SnS/bilayer graphene (AB-stacked) and monolayer SnS/graphene/monolayer SnS van der Waals (vdW) heterostructures. Electronic properties of all components of the vdW heterostructures are well preserved, which reflects the weakness of the vdW interaction. In the cases of bilayer SnS/graphene and bilayer SnS/bilayer graphene (AA-stacked), an Ohmic contact is formed which can be turned first into p-type and then into n-type Schottky c…
We have found that the Berry phase of bilayer graphene becomes from 2$π$ estimated by Shubnikov-de Haas oscillations when the A-B stacked pristine bilayer graphene experiences the Li-intercalation and sequential Li-desorption process in ultrahigh vacuum. Furthermore, the mobility of such processed bilayer graphene increases around four times larger, ~ 8,000 cm2/V$\cdot$s, than that of the pristine bilayer graphene. This is mainly due to increment of the scattering time and decrement of the cyclotron mass, which can be interpreted as a result of the change of the stacking structure of bilayer g…
We investigate band-gap tuning of bilayer graphene between hexagonal boron nitride sheets, by external electric fields. Using density functional theory, we show that the gap is continuously tunable from 0 to 0.2 eV, and is robust to stacking disorder. Moreover, boron nitride sheets do not alter the fundamental response from that of free-standing bilayer graphene, apart from additional screening. The calculations suggest that the graphene-boron nitride heterostructures could provide a viable route to graphene-based electronic devices.
We examine the quantum Hall effect in bilayer graphene grown on Cu substrates by chemical vapor deposition. Spatially resolved Raman spectroscopy suggests a mixture of Bernal (A-B) stacked and rotationally faulted (twisted) domains. Magnetotransport measurements performed on bilayer domains with a wide 2D band reveal quantum Hall states (QHSs) at filling factors $ν=4, 8, 12$ consistent with a Bernal stacked bilayer, while magnetotransport measurements in bilayer domains defined by a narrow 2D band show a superposition of QHSs of two independent monolayers. The analysis of the Shubnikov-de Haas…
We study the mid-infrared plasmonic response in Bernal-stacked bilayer graphene. Unlike its monolayer counterpart, bilayer graphene accommodates optically active phonon modes and a resonant interband transition at infrared frequencies. They strongly modifies the plasmonic properties of bilayer graphene, leading to Fano-type resonances, giant plasmonic enhancement of infrared phonon absorption, narrow window of optical transparency, and a new plasmonic mode at higher energy than the classical plasmon.
Based on ab initio calculations, we study the effect of intercalating twisted bilayer graphene with carbon. Surprisingly, we find that the intercalant pulls the atoms in the two layers closer together locally when placed in certain regions in between the layers, and the process is energetically favorable as well. This arises because in these regions of the supercell, the local environment allows the intercalant to form tetrahedral bonding with nearest atoms in the layers. Intercalating AB- or AA-bilayer graphene with carbon does not produce this effect; therefore, the nontrivial effect owes it…
We study the Landau quantization of the electronic spectrum for graphene bilayers that are rotationally faulted to produce periodic superlattices. Commensurate twisted bilayers exist in two families distinguished by their sublattice exchange parity. We show that these two families exhibit distinct Landau quantized spectra distinguished both by the interlayer coupling of their zero modes and by an amplitude modulation of their spectra at energies above their low energy interlayer coherence scales. These modulations can provide a powerful experimental probe of the magnitude of a weak coherence s…
The interlayer magnetic interaction in bilayer CrI$_3$ plays a crucial role for its device applications. In this work, we studied the interlayer magnetic interaction in $π/3$-twisted bilayer CrI$_3$ using first-principles calculations. Our calculations show that the interlayer coupling can be ferromagnetic or antiferromagnetic depending crucially on lateral shift. The strongest antiferromagnetic interlayer interaction appears in the $\bar{A}A$-stacking. The magnetic force theory calculations demonstrate that such an antiferromagnetic interaction is dominanted by the $e_g$-$e_g$ channel. Partic…
We have studied how a generic bilayer kagome lattice behave upon layer rotation. We employed a Tight Binding model with one orbital per site and found (i) for low rotational angles, and at low energies, the same flat bands structure like in twisted bilayer graphene; though, for a larger value of the magic angle. Moreover, (ii) at high energies, due to the superstructure symmetry regions, we found the characteristics three band dispersion of the kagome lattice. In the latter, its band width decreases for lower angles confining them within a few meV. Therefore, we found in twisted kagome lattice…
We consider the electronic structure of a slightly twisted graphene bilayer and show the coexistence of van Hove singularities (VHSs) and superlattice Dirac points in a continuum approximation. The graphene-on-graphene moiré pattern gives rise to a periodic electronic potential, which leads to the emergence of the superlattice Dirac points due to the chiral nature of the charge carriers. Owning to the distinguishing real and reciprocal structures, the sublattice exchange even and odd structures of the twisted graphene bilayer (the two types of commensurate structures) result in two different s…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($θ$) close to 0$^\circ$ and at both the valence and conduction band edges for $θ$ close to 60$^\circ$, and have distinct origins. For$ θ$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moiré superlattice is…
Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bila…
A perpendicular electric field breaks the layer symmetry of Bernal-stacked bilayer graphene, resulting in the opening of a band gap and a modification of the effective mass of the charge carriers. Using scanning tunneling microscopy and spectroscopy, we examine standing waves in the local density of states of bilayer graphene formed by scattering from a bilayer/trilayer boundary. The quasiparticle interference properties are controlled by the bilayer graphene band structure, allowing a direct local probe of the evolution of the band structure of bilayer graphene as a function of electric field…
We derive core-level spectra for doped free-standing bilayer graphene. Numerical results are presented for all nine combinations of the doping concentrations $10^{12}\rm{cm}^{-2}$, $10^{13}\rm{cm}^{-2}$, and $10^{14}\rm{cm}^{-2}$ in the two graphene sheets and we compare the results to the reference spectra for monolayer graphene. We furthermore discuss the spectrum of single-particle inter-band and intra-band excitations in the $ωq$-plane, and show how the dispersion curves of the collective modes are modified in the bilayer system.
The perfect transmission in graphene monolayer and the perfect reflection in Bernal graphene bilayer for electrons incident in the normal direction of a potential barrier are viewed as two incarnations of the Klein paradox. Here we show a new and unique incarnation of the Klein paradox. Owing to the different chiralities of the quasiparticles involved, the chiral fermions in twisted graphene bilayer shows adjustable probability of chiral tunnelling for normal incidence: they can be changed from perfect tunnelling to partial/perfect reflection, or vice versa, by controlling either the height of…
The electronic dispersion of a graphene bilayer is highly dependent on rotational mismatch between layers and can be further manipulated by electrical gating. This allows for an unprecedented control over electronic properties and opens up the possibility of flexible band structure engineering. Here we present novel magnetotransport data in a twisted bilayer, crossing the energetic border between decoupled monolayers and coupled bilayer. In addition a transition in Berry phase between pi and 2pi is observed at intermediate magnetic fields. Analysis of Fermi velocities and gate induced charge c…
We theoretically investigated phonon dispersion in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. The calculations were performed using the Born-von-Karman model for the intra-layer atomic interactions and the Lennard-Jones potential for the inter-layer interactions. It was found that the stacking order affects the out-of-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA- or AB-stacked bilayer graphene appears in the phonon frequencies range 90 - 110 1/cm. Twisting bilayer graphene…
We investigate the atomic-scale tunneling characteristics of bilayer graphene on silicon carbide using the scanning tunneling microscopy. The high-resolution tunneling spectroscopy reveals an unexpected negative differential resistance (NDR) at the Dirac energy, which spatially varies within the single unit cell of bilayer graphene. The origin of NDR is explained by two near-gap van Hove singularities emerging in the electronic spectrum of bilayer graphene under a transverse electric field, which are strongly localized on two sublattices in different layers. Furthermore, defects near the tunne…
Bilayer graphene contains, compared to graphene monolayer, an additional graphene sheet and, therefore, extra degrees of freedom, making it a unique system for complex electronic states to emerge. Here, we show that there are two types of domain walls, i.e., coupling domain wall and potential domain wall, in gapped graphene bilayers, which make microscopic electronic properties of the bilayers varying spatially. The coupling domain wall separates two graphene bilayer regions with different interlayer coupling strengths and the potential domain wall is a boundary separating two adjacent regions…
Theory of scattering of massive chiral fermions in bilayer graphene by radial symmetric potential is developed. It is shown that in the case when the electron wavelength is much larger than the radius of the potential the scattering cross-section is proportional to the electron wavelength. This leads to the mobility independent on the electron concentration. In contrast with the case of single-layer, neutral and charged defects are, in general, equally relevant for the resistivity of the bilayer graphene.
We analyze the response of bilayer graphene to an external transverse electric field using a variational method. A previous attempt to do so in a recent paper by Falkovsky [Phys. Rev. B 80, 113413 (2009)] is shown to be flawed. Our calculation reaffirms the original results obtained by one of us [E. McCann, Phys. Rev. B 74, 161403(R) (2006)] by a different method. Finally, we generalize these original results to describe a dual-gated bilayer graphene device.
Atomic defects have a significant impact in the low-energy properties of graphene systems. By means of first-principles calculations and tight-binding models we provide evidence that chemical impurities modify both the normal and the superconducting states of twisted bilayer graphene. A single hydrogen atom attached to the bilayer surface yields a triple-point crossing, whereas self-doping and three-fold symmetry-breaking are created by a vacant site. Both types of defects lead to time-reversal symmetry-breaking and the creation of local magnetic moments. Hydrogen-induced magnetism is found to…
Coherent motion of the electrons in the Bloch states is one of the fundamental concepts of the charge conduction in solid state physics. In layered materials, however, such a condition often breaks down for the interlayer conduction, when the interlayer coupling is significantly reduced by e.g. large interlayer separation. We report that complete suppression of coherent conduction is realized even in an atomic length scale of layer separation in twisted bilayer graphene. The interlayer resistivity of twisted bilayer graphene is much higher than the c-axis resistivity of Bernal-stacked graphite…
We develop a theory for density, disorder, and temperature dependent electrical conductivity of bilayer graphene in the presence of long-range charged impurity scattering as well as an additional short-range disorder of independent origin, establishing that both scattering mechanisms contribute significantly to determining bilayer transport properties. We find that although strong screening properties of bilayer graphene lead to qualitative differences with the corresponding single layer situation, both systems exhibit the linearly density dependent conductivity at high density and the minimum…
Bilayer graphene is a promising material for radio-frequency transistors because its energy gap might result in a better current saturation than the monolayer graphene. Because the great deal of interest in this technology, especially for flexible radio-frequency applications, gaining control of it requires the formulation of appropriate models for the drain current, charge and capacitance. In this work we have developed them for a dual-gated bilayer graphene field-effect transistor. A drift-diffusion mechanism for the carrier transport has been considered coupled with an appropriate field-eff…
The electronic structure of bilayer graphene is investigated from a resonant Raman study using different laser excitation energies. The values of the parameters of the Slonczewski-Weiss-McClure model for graphite are measured experimentally and some of them differ significantly from those reported previously for graphite, specially that associated with the difference of the effective mass of electrons and holes. The splitting of the two TO phonon branches in bilayer graphene is also obtained from the experimental data. Our results have implications for bilayer graphene electronic devices.
The electronic structure of the zig-zag bilayer strip is analyzed. The electronic spectra of the bilayer strip is computed. The dependence of the edge state band flatness on the bilayer width is found. The density of states at the Fermi level is analytically computed. It is shown that it has the singularity which depends on the width of the bilayer strip. There is also asymmetry in the density of states below and above the Fermi energy.
The generalized tight-binding model is developed to investigate the magneto-electronic properties in twisted bilayer graphene system. All the interlayer and intralayer atomic interactions are included in the Moire superlattice. The twisted bilayer graphene system is a zero-gap semiconductor with double-degenerate Dirac-cone structures, and saddle-point energy dispersions appearing at low energies for cases of small twisting angles. There exist rich and unique magnetic quantization phenomena, in which many Landau-level subgroups are induced due to specific Moire zone folding through modulating …
Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such lo…
Ultraflat bands in twisted bilayers of two-dimensional materials have potential to host strong correlations, including the Mott-insulating phase at half-filling of the band. Using first principles density functional theory calculations, we show the emergence of ultraflat bands at the valence band edge in twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. The computed band widths, 5 meV and 23 meV for 56.5$^\circ$ and 3.5$^\circ$ twist angles respectively, are comparable to that of twisted bilayer graphene near 'magic' angles. Large structural transformations in the Moiré …
Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structures related to order-induced topological characters. We use our results to estimate Ginzburg-Landau model parameters and transition temperatures for the ordered states of bilayer graphene.
We predict twisted double bilayer graphene to be a versatile platform for the realization of fractional Chern insulators readily targeted by tuning the gate potential and the twist angle. Remarkably, these topologically ordered states of matter, including spin singlet Halperin states and spin polarized states in Chern number $\mathcal C=1$ and $\mathcal{C}= 2$ bands, occur at high temperatures and without the need for an external magnetic field.
In a system with inversion symmetry broken, a second-order nonlinear Hall effect can survive even in the presence of time-reversal symmetry. In this work, we show that a giant nonlinear Hall effect can exist in twisted bilayer WTe2 system. The Berry curvature dipole of twisted bilayer WTe2 (θ = 29.4°) can reach up to ~1400 Å, which is much larger than that in previously reported nonlinear Hall systems. In twisted bilayer WTe2 system, there exists abundant band anticrossings and band inversions around the Fermi level, which brings a complicated distribution of Berry curvature, and leading to th…
Using first-principles techniques, we calculate the renormalization of the electron Fermi velocity and the vibrational lifetimes arising from electron-phonon interactions in doped bilayer graphene and in graphite and compare the results with the corresponding quantities in graphene. For similar levels of doping, the Fermi velocity renormalization in bilayer graphene and in graphite is found to be approximately 30% larger than that in graphene. In the case of bilayer graphene, this difference is shown to arise from the interlayer interaction. We discuss our findings in the light of recent photo…
By using the first-principles method based on density of functional theory, we study the electronic properties of twisted bilayer graphene with some specific twist angles and interlayer spacings. With the decrease of the twist angle(the unit cell becomes larger), the energy band becomes narrower and Coulomb repulsion increases, leading to the enhancement of electronic correlation; On the other hand, as the interlayer spacing decreases and the interlayer coupling becomes stronger, the correlation becomes stronger. By tuning the interlayer coupling, we can realize the strongly correlated state w…
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as function…
Effect of electric field on the band structures of graphene/BN and BN/BN bilayers is investigated within the framework of density functional theory. A relatively large degree of modulation is predicted for the graphene/BN bilayer. The calculated band gap of the graphene/BN bilayer increases with applied electric field, which is not the case of BN/BN bilayer; its band gap decreases with the applied field. Both features in the bilayers considered appear to be related to the nature of the conduction band and the redistribution of the electronic charge of the bilayer systems under the influence of…
The chemical modification of graphene with adatoms is of importance for nanoelectronics applications. Based on first-principles density-functional theory calculations with including van der Waals interactions, we present a comparative study of the diffusion characteristics of oxygen (O) and fluorine (F) atoms both on graphene and between the layers of bilayer graphene. We find that O and F atoms have lower binding energies between the layers of bilayer graphene compared to on graphene. Interestingly, the calculated diffusion barrier for the O atom slightly increases from 0.81 eV on graphene to…
We calculate thermopower of clean and impure bilayer graphene systems. Opening a band gap through the application of an external electric field is shown to greatly enhance the thermopower of bilayer graphene, which is more than four times that of the monolayer graphene and gapless bilayer graphene at room temperature. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Temperature dependence of the thermopower is also analyzed.
High-harmonic generation (HHG) in solids is an emerging method to probe ultrafast electron dynamics in solids at attosecond timescale. In this work, we study HHG from monolayer and bilayer graphene. Bilayer graphenes with AA and AB stacking are considered in this work. It is found that the monolayer and bilayer graphenes exhibit significantly different harmonic spectra. The difference in the spectra is attributed to the interlayer coupling between the two layers. Also, the intraband and interband contributions to the total harmonic spectrum play a significant role. Moreover, interesting polari…
A cheap and flexible method is introduced that enables the epitaxial growth of bilayer graphene on Pt(111) by sequential chemical vapour deposition. Extended regions of two stacked graphene sheets are obtained by, first, the thermal decomposition of ethylene and the subsequent formation of graphene. In the second step, a sufficiently thick Pt film buries the first graphene layer and acts as a platform for the fabrication of the second graphene layer in the third step. A final annealing process then leads to the diffusion of the first graphene sheet to the surface until the bilayer stacking wit…
Low-frequency 1/f noise is ubiquitous, and dominates the signal-to-noise performance in nanodevices. Here we investigate the noise characteristics of single-layer and bilayer graphene nano-devices, and uncover an unexpected 1/f noise behavior for bilayer devices. Graphene is a single layer of graphite, where carbon atoms form a 2D honeycomb lattice. Despite the similar composition, bilayer graphene (two graphene monolayers stacked in the natural graphite order) is a distinct 2D system with a different band structure and electrical properties. In graphene monolayers, the 1/f noise is found to f…
In this article, based on first-principles calculations, we systematically study functionalization induced diamonization of graphene bilayer and graphene-BN hybrid bilayer. With single-side functionalization, the diamondized structures are magnetic semiconductor. Interestingly, if both sides of the bilayer are functionalized, diamondization becomes spontaneous without a barrier. On the other hand, when the bottom layer of the bilayer graphene is replaced by a single hexagonal BN layer, the diamondized structure becomes nonmagnetic metal. The tunable electronic and magnetic properties pave new …
Tailoring the interlayer twist angle of bilayer graphene (BLG) has a significant influence on its electronic properties, including superconductivity, topological transitions, ferromagnetic states and correlated insulating states. These exotic electronic properties are sensitively dependent on the work functions of bilayer graphene samples. Here, the twisted angle-dependent work functions of CVD-grown twisted bilayer graphene (tBLG) are detailed investigated by Kelvin Probe Force Microscopy (KPFM) in combination with Raman spectra. The thickness-dependent surface potentials of Bernal-stacked mu…
Evidence of flat-band magnetism and half-metallicity in compressed twisted bilayer graphene is provided with first-principles calculations. We show that dynamic band-structure engineering in twisted bilayer graphene is possible by controlling the chemical composition with extrinsic doping, the interlayer coupling strength with pressure, and the magnetic ordering with external electric field. By varying the rotational order and reducing the interlayer separation an unbalanced distribution of charge density resulting in the spontaneous apparition of localized magnetic moments without disrupting …
The electronic properties of the twisted InSe bilayer are studied by large-scale density functional theory. Spectral Function Unfolding reveals that the electronic structure of the twisted system can be described in terms of a combination of features of the bandstructures of the aligned InSe bilayer with different stacking configurations, enabling predictions of the band gap and the effective mass for holes. The effective mass for holes in the twisted InSe bilayer is shown to be influenced primarily by the interlayer distance. The intralayer and interlayer exciton binding energies are thus cal…
We present first-principles calculations of many-electron effects on the optical response of graphene, bilayer graphene, and graphite employing the GW-Bethe Salpeter equation approach. We find that resonant excitons are formed in these two-dimensional semimetals. The resonant excitons give rise to a prominent peak in the absorption spectrum near 4.5 eV with a different line shape and significantly redshifted peak position from those of an absorption peak arising from interband transitions in an independent quasiparticle picture. In the infrared regime, our calculated optical absorbance per gra…
