Coherent excitation of shear phonons in van der Waals layered materials is a non-destructive mechanism to fine-tune the electronic state of the system. We develop a diagrammatic theory for the displacive Raman force and apply it to the shear phonon's dynamics. We obtain a rectified Raman force density in bilayer graphene of the order of ${\cal F}\sim 10{\rm nN/nm^2}$ leading to a giant shear displacement $Q_0 \sim 50$pm for an intense infrared laser. We discuss both circular and linear displacive Raman forces. We show that the laser frequency and polarization can effectively tune $Q_0$ in different electronic doping, temperature, and scattering rates. We reveal that the finite $Q_0$ induces a Dirac crossing pair in the low-energy dispersion that photoemission spectroscopy can probe. Our finding provides a systematic pathway to simulate and analyze the coherent manipulation of staking order in the heterostructures of layered materials by laser irradiation.
The line shape of the double-resonant $2D$ Raman mode in bilayer graphene is often considered to be characteristic for a certain laser excitation energy. Here, in a joint experimental and theoretical study, we analyze the dependence of the double-resonant Raman scattering processes in bilayer graphene on the electronic broadening parameter $γ$. We demonstrate that the ratio between symmetric and anti-symmetric scattering processes sensitively depends on the lifetime of the electronic states, explaining the experimentally observed variation of the complex $2D$-mode line shape.
We compare the main feature of the measured Raman scattering spectra from single layer graphene with a bilayer in which the two layers are arbitrarily misoriented. The profiles of the 2D bands are very similar having only one component, contrary to the four found for commensurate Bernal bilayers. These results agree with recent theoretical calculations and point to the similarity of the electronic structures of single layer graphene and misoriented bilayer graphene. Another new aspect is that the dependance of the 2D frequency on the laser excitation energy is different in these two latter sys…
We present complete calculations of the two-phonon Raman bands of bilayer graphene, including all overtone and combination modes, within a density-functional tight-binding model. Based on our results, we assign unambiguously the observed two-phonon Raman bands to two-phonon modes, thus resolving the existing controversies. In particular, we show that both overtone and combination modes have essential contribution to the 2D band, bringing about specific modifications of the band shape. We argue that a mid-range two-phonon Raman band, previously assigned to the 2ZO mode, should be assigned to th…
We report a symmetry resolved electronic Raman scattering (ERS) study of a bilayer graphene device under gate voltage. We show that the ERS continuum is dominated by interband chiral excitations of $A_{2}$ symmetry and displays a characteristic Pauli-blocking behavior similar to the monolayer case. Crucially, we show that non-chiral excitations make a vanishing contribution to the Raman cross-section due to destructive interference effects in the Raman amplitude matrix elements. This is in a marked contrast to optical absorption measurements and opens interesting venues for the use of Raman sc…
In this letter we use graphene bubbles to study the Raman spectrum of graphene under biaxial (e.g. isotropic) strain. Our Gruneisen parameters are in excellent agreement with the theoretical values. Discrepancy in the previously reported values is attributed to the interaction of graphene with the substrate. Bilayer balloons (intentionally pressurized membranes) have been used to avoid the effect of the substrate and to study the dependence of strain on the inter-layer interactions.
In this work we study the behavior of the optical phonon modes in bilayer graphene devices by applying top gate voltage, using Raman scattering. We observe the splitting of the Raman G band as we tune the Fermi level of the sample, which is explained in terms of mixing of the Raman (Eg) and infrared (Eu) phonon modes, due to different doping in the two layers. We theoretically analyze our data in terms of the bilayer graphene phonon self-energy which includes non-homogeneous charge carrier doping between the graphene layers. We show that the comparison between the experiment and theoretical mo…
Two new Raman modes below 100 cm^-1 are observed in twisted bilayer graphene grown by chemical vapor deposition. The two modes are observed in a small range of twisting angle at which the intensity of the G Raman peak is strongly enhanced, indicating that these low energy modes and the G Raman mode share the same resonance enhancement mechanism, as a function of twisting angle. The 94 cm^-1 mode (measured with a 532 nm laser excitation) is assigned to the fundamental layer breathing vibration (ZO (prime) mode) mediated by the twisted bilayer graphene lattice, which lacks long-range translation…
We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong non-linear behavior in the transport characteristics. The effective transport gap is typically two orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in …
The dispersion of phonons and the electronic structure of graphene systems can be obtained experimentally from the double-resonance (DR) Raman features by varying the excitation laser energy. In a previous resonance Raman investigation of graphene, the electronic structure was analyzed in the framework of the Slonczewski-Weiss-McClure (SWM) model, considering the outer DR process. In this work we analyze the data considering the inner DR process, and obtain SWM parameters that are in better agreement with those obtained from other experimental techniques. This result possibly shows that there …
In this work, we study the Raman spectra of twisted bilayer graphene samples as a function of their twist-angles ($θ$), ranging from 0.03$^\circ$ to 3.40$^\circ$, where local $θ$ are determined by analysis of their associated moire 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 wavele…
We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the e…
The polarization dependence of the double resonant Raman scattering (2D) band in bilayer graphene (BLG) is studied as a function of the excitation laser energy. It has been known that the complex shape of the 2D band of BLG can be decomposed into four Lorentzian peaks with different Raman frequency shifts attributable to four individual scattering paths in the energy-momentum space. From our polarization dependence study, however, we reveal that each of the four different peaks is actually doubly degenerate in its scattering channels, i.e., two different scattering paths with similar Raman fre…
By computing the double-resonant Raman scattering cross-section completely from first principles and including electron-electron interaction at the $GW$ level, we unravel the dominant contributions for the double-resonant 2D-mode in bilayer graphene. We show that, in contrast to previous works, the so-called inner processes are dominant and that the 2D-mode lineshape is described by three dominant resonances around the $K$ point. We show that the splitting of the TO phonon branch in $Γ-K$ direction, as large as 12 cm$^{-1}$ in $GW$ approximation, is of great importance for a thorough descripti…
The band structure of bilayer graphene is tunable by introducing a relative twist angle between the two layers, unlocking exotic phases, such as superconductor and Mott insulator, and providing a fertile ground for new physics. At intermediate twist angles around 10°, highly degenerate electronic transitions hybridize to form excitonic states, a quite unusual phenomenon in a metallic system. We probe the bright exciton mode using resonant Raman scattering measurements to track the evolution of the intensity of the graphene Raman G peak, corresponding to the E2g phonon. By cryogenically cooling…
A Raman study of a back gated bilayer graphene sample is presented. The changes in the Fermi level induced by charge transfer splits the Raman G-band, hardening its higher component and softening the lower one. These two components are associated with the symmetric (S) and anti-symmetric vibration (AS) of the atoms in the two layers, the later one becoming Raman active due to inversion symmetry breaking. The phonon hardening and softening are explained by considering the selective coupling of the S and AS phonons with interband and intraband electron-hole pairs.
We use angle-resolved photoemission spectroscopy to investigate the electronic structure of bilayer graphene at high n-doping and extreme displacement fields, created by intercalating epitaxial monolayer graphene on silicon carbide with magnesium to form quasi-freestanding bilayer graphene on magnesium-terminated silicon carbide. Angle-resolved photoemission spectroscopy reveals that upon magnesium intercalation, the single massless Dirac band of epitaxial monolayer graphene is transformed into the characteristic massive double-band Dirac spectrum of quasi-freestanding bilayer graphene. Analys…
In the bilayer ReS$ _{2} $ channel of a field-effect transistor (FET), we demonstrate using Raman spectroscopy that electron doping (n) results in softening of frequency and broadening of linewidth of the in-plane vibrational modes, leaving out-of-plane vibrational modes unaffected. Largest change is observed for the in-plane Raman mode at $\sim$ 151 cm$^{-1} $, which also shows doping induced Fano resonance with the Fano parameter 1/q = -0.17 at doping concentration of $\sim 3.7\times10^{13}$ cm$^{-2} $. A quantitative understanding of our results is provided by first-principles density funct…
The electronic structure of bilayer graphene is investigated from a resonant Raman study using different laser excitation energies. The values of the parameters of the Slonczewski-Weiss-McClure model for graphite are measured experimentally and some of them differ significantly from those reported previously for graphite, specially that associated with the difference of the effective mass of electrons and holes. The splitting of the two TO phonon branches in bilayer graphene is also obtained from the experimental data. Our results have implications for bilayer graphene electronic devices.
We report the observation of anomalously strong 2D band in twisted bilayer graphene (tBLG) with large rotation angles under 638-nm and 532-nm visible laser excitation. The 2D band of tBLG can reach four times as opposed to two times as strong as that of single layer graphene. The same tBLG samples also exhibit rotation dependent G-line resonances and folded phonons under 364-nm UV laser excitation. We attribute this 2D band Raman enhancement to the constructive quantum interference between two double-resonance Raman pathways which are enabled by nearly degenerate Dirac band in tBLG Moiré super…
The temperature evolution of the resonant Raman scattering from high-quality bilayer 2H-MoS$_{2}$ encapsulated in hexagonal BN flakes is presented. The observed resonant Raman scattering spectrum as initiated by the laser energy of 1.96 eV, close to the A excitonic resonance, shows rich and distinct vibrational features that are otherwise not observed in non-resonant scattering. The appearance of 1$^{st}$ and 2$^{nd}$ order phonon modes is unambiguously observed in a broad range of temperatures from 5 K to 320 K. The spectrum includes the Raman-active modes, $i.e.$ E$_\textrm{1g}^{2}$($Γ$) and…
Hybridisation of electronic bands of two-dimensional materials, assembled into twistronic heterostructures, enables one to tune their optoelectronic properties by selecting conditions for resonant interlayer hybridisation. Resonant interlayer hybridisation qualitatively modifies the excitons in such heterostructures, transforming these optically active modes into superposition states of interlayer and intralayer excitons. For MoSe$_2$/WSe$_2$ heterostructures, strong hybridization occurs between the holes in the spin-split valence band of WSe$_2$ and in the top valence band of MoSe$_2$, especi…
Polarization resolved micro-Raman spectroscopy was carried out at the edges of bilayer graphene. We find strong dependence of the intensity of the G band on the incident laser polarization, with its intensity dependence being 90 degrees out of phase for the armchair and zigzag case, in accordance with theoretical predictions. For the case of mixed-state edges we demonstrate that the polarization contrast reflects the fractional composition of armchair and zigzag edges, providing a monitor of edge purity, which is an important parameter for the development of efficient nanoelectronic devices.
We investigate the ultralow-frequency Raman response of atomically thin ReS2, a special type of two-dimensional (2D) semiconductors with unique distorted 1T structure. Bilayer and few-layer ReS2 exhibit rich Raman spectra at frequencies below 50 cm-1, where a panoply of interlayer shear and breathing modes are observed. The emergence of these interlayer phonon modes indicate that the ReS2 layers are coupled and stacked orderly, in contrast to the general belief that the ReS2 layers are decoupled from one another. While the interlayer breathing modes can be described by a linear chain model as …
Model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and film/substrate systems. We show that three ensembles of parallel screw dislocations are sufficient both to describe the rotation of the layers as a whole, and for the vortex-like displacements resulting from elastic relaxation. The results give a clear explanation of the observed features of the structural state such as vortices, accompanied by alternating s…
Van der Waals layered materials with well-defined twist angles between the crystal lattices of individual layers have attracted increasing attention due to the emergence of unexpected material properties. As many properties critically depend on the exact twist angle and its spatial homogeneity, there is a need for a fast and non-invasive characterization technique of the local twist angle, to be applied preferably right after stacking. We demonstrate that confocal Raman spectroscopy can be utilized to spatially map the twist angle in stacked bilayer graphene for angles between 6.5° and 8° when…
The most important bands for the evaluation of strain in graphene (the 2D and 2D prime modes) are investigated. It is shown that for Bernal-stacked bilayers, the two-phonon Raman features have three different components that can be assigned to processes originating solely from the top graphene layer, bottom graphene layer, and from a combination of processes originating both from the top and bottom layers. The individual components of the 2D and 2D prime modes are disentangled. The reported results enable addressing the properties of individual graphene layers in isotopically labelled turbostr…
University of Warsaw（华沙大学）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；Peking University Shenzhen Graduate School（北京大学深圳研究生院）；CNRS（法国国家科学研究中心）
The dispersion of electrons and phonons near the K point of bilayer graphene was investigated in a resonant Raman study using different laser excitation energies in the near infrared and visible range. The electronic structure was analyzed within the tight-binding approximation, and the Slonczewski-Weiss-McClure (SWM) parameters were obtained from the analysis of the dispersive behavior of the Raman features. A softening of the phonon branches was observed near the K point, and results evidence the Kohn anomaly and the importance of considering electron-phonon and electron-electron interaction…
We present a novel measurement approach which combines the electrical characterization of solution-gated field effect transistors based on epitaxial bilayer graphene on 4H-SiC (0001) with simultaneous Raman spectroscopy. By changing the gate voltage, we observed Raman signatures related to the resonant electron-phonon coupling. An analysis of these Raman bands enabled the extraction of the geometrical capacitance of the system and an accurate calculation of the Fermi levels for bilayer graphene. An intentional application of higher gate voltages allowed us to trigger electrochemical reactions,…
With the increasing interest in twisted bilayer graphene (tBLG) of the past years, fast, reliable, and non-destructive methods to precisely determine the twist angle are required. Raman spectroscopy potentially provides such method, given the large amount of information about the state of the graphene that is encoded in its Raman spectrum. However, changes in the Raman spectra induced by the stacking order can be very subtle, thus making the angle identification tedious. In this work, we propose the use of machine learning (ML) analysis techniques for the automated classification of the Raman …
Raman measurements on monolayer graphene folded back upon itself as an ordered but skew-stacked bilayer (i.e. with interlayer rotation) presents new mechanism for Raman scattering in sp2 carbons that arises in systems that lack coherent AB interlayer stacking. Although the parent monolayer does not exhibit a D-band, the interior of the skewed bilayer produces a strong two-peak Raman feature near 1350 cm-1; one of these peaks is non-dispersive, unlike all previously observed D-band features in sp2 carbons. Within a double-resonant model of Raman scattering, these unusual features are consistent…
We use Scanning Gate Microscopy to demonstrate the presence of localized states arising from potential inhomogeneities in a 50nm-wide, gate-defined conducting channel in encapsulated bilayer graphene. When imaging the channel conductance under the influence of a local tip-induced potential, we observe ellipses of enhanced conductance as a function of the tip position. These ellipses allow us to infer the location of the localized states and to study their dependence on the displacement field. For large displacement fields, we observe that localized states tend to occur halfway into the channel…
We study the variations of electron-phonon coupling and their spectroscopic consequences in response to sliding of two layers in bilayer graphene using first-principles calculations and a model Hamiltonian. Our study shows that the long wave-length optical phonon modes change in a sensitive and unusual way depending on the symmetry as well as the parity of sliding atomic structures and that, accordingly, Raman- and infrared-active optical phonon modes behave differently upon the direction and size of the sliding. The renormalization of phonon modes by the interlayer electronic coupling is show…
In the presence of a finite interlayer displacement field bilayer graphene has an energy gap that is dependent on stacking and largest for the stable AB and BA stacking arrangements. When the relative orientations between layers are twisted through a small angle to form a moir$\mathrm{\acute{e}}$ pattern, the local stacking arrangement changes slowly. We show that for non-zero displacement fields the low-energy physics of twisted bilayers is captured by a phenomenological helical network model that describes electrons localized on domain walls separating regions with approximate AB and BA stac…
Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the $\mathcal{N}{=}2$ Landau levels of Bernal-stacked bilayer graphene
Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；Department of Physics, Indian Institute of Technology Bombay（印度理工学院孟买分校物理系）；Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）
We report phonon renormalisation in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping, as a result of the non-adiabatic Kohn anomaly at the $Γ$ point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This results in a change of slope in the variation of G peak position with doping, which allows a direct measurement of the interlayer coupling strength.
We report the influence of uniaxial tensile mechanical strain in the range 0-2.2% on the phonon spectra and bandstructures of monolayer and bilayer molybdenum disulfide (MoS2) two-dimensional crystals. First, we employ Raman spectroscopy to observe phonon softening with increased strain, breaking the degeneracy in the E' Raman mode of MoS2, and extract a Grüneisen parameter of ~1.06. Second, using photoluminescence spectroscopy we measure a decrease in the optical band gap of MoS2 that is roughly linear with strain, ~45 meV% strain for monolayer MoS2 and ~120 meV% strain for bilayer MoS2. Thir…
Twisted bilayer graphene (TBLG) has emerged as an exciting new material with tunable electronic properties ranging from superconductivity to correlated insulating phases. But current methods of fabrication and identification of TBLG are painstaking and laborious. In this work, we combine Raman spectroscopy with the Gaussian mixture model (GMM) data clustering algorithm to identify areas with particular twist angles, from a TBLG sample with a mixture of orientations. We present two approaches to this cluster analysis: training the GMM on Raman parameters returned by peak fits, and on full Raman…
We present the first Raman spectroscopic study of Bernal bilayer graphene flakes under uniaxial tension. Apart from a purely mechanical behavior in flake regions where both layers are strained evenly, certain effects stem from inhomogeneous stress distribution across the layers. These phenomena such as the removal of inversion symmetry in bilayer graphene may have important implications in the band-gap engineering providing an alternative route to induce the formation of a band-gap.
One of the greatest issues of nanoelectronics today is how to control the heating of the components. Graphene is a promising material in this area and it is essential to study its thermal properties. Here, the effect of heating a bilayer structure was investigated using in situ Raman spectroscopy. In order to observe the effects on each individual layer, an isotopically labelled bilayer graphene was synthesized where the two layers are composed of different carbon isotopes. Therefore, the frequency of the phonons in the Raman spectra is shifted in relation to each other. This technique was use…
The lattice contraction phenomenon found in time resolved X-ray diffraction and electron diffraction experiments is usually considered to be caused by photo-generated carriers. However, the quantum calculation under finite-time boundary conditions leads to a transient Raman process that directly connects optical transitions and lattice displacements. The lattice contraction phenomenon and the coherent phonon phenomenon can be explained well by the process.
The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are stu…
Non-dispersive, inter-layer interaction induced Raman peaks (I bands) -- in the region of the D band -- have been observed recently for bilayer graphene, when the two layers were rotated with respect to each other. Here, similar observations for double-walled carbon nanotubes (DWCNTs) are theoretically predicted. The prediction is based on double resonance theory, involving non-zone-centered phonons, and the effect of disorder is replaced by interaction between the two tubes.
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…
Twisted bilayer graphene (tBLG) provides us with a large rotational freedom to explore new physics and novel device applications, but many of its basic properties remain unresolved. Here we report the synthesis and systematic Raman study of tBLG. Chemical vapor deposition was used to synthesize hexagon- shaped tBLG with a rotation angle that can be conveniently determined by relative edge misalignment. Superlattice structures are revealed by the observation of two distinctive Raman features: folded optical phonons and enhanced intensity of the 2D-band. Both signatures are strongly correlated w…
We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase $2π$. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and non-Bernal stacking.
