The dominant phonon wavevectors $q^{*}$ probed by the 2D Raman mode of graphene are highly anisotropic and rotate with the orientation of the polarizer:analyzer direction relative to the lattice. The corresponding electronic transitions connect the electronic equibandgap contours where the product of the ingoing and outgoing optical matrix elements is strongest, showing a finite component along $\bm{K}-\bmΓ$ that sensitively determines $q^{*}$. We revoke the notion of 'inner' and 'outer' processes. Our findings explain the splitting of the 2D mode of graphene under uniaxial tensile strain. The splitting originates from a strain-induced distortion of the phonon dispersion; changes in the electronic band structure and resonance conditions are negligeable for the 2D Raman spectrum.
Electrostatic gating offers elegant ways to simultaneously strain and dope atomically thin membranes. Here, we report on a detailed \textit{in situ} Raman scattering study on graphene, suspended over a Si/SiO$_2$ substrate. In such a layered structure, the intensity of the Raman G- and 2D-mode features of graphene are strongly modulated by optical interference effects and allow an accurate determination of the electrostatically-induced membrane deflection, up to irreversible collapse. The membrane deflection is successfully described by an electromechanical model, which we also use to provide …
Monolayer WTe2 attracts rapidly growing interests for its large-gap quantum spin Hall effect,which enables promising apllications in flexible logic devices. Due to one-dimensional W-W chains,1T'-WTe2 exhibits unique anisotropic structure and promising properties, which can be modified by simply applying strains. Based on the first-principles simulations, we show that phonon branch undergoes soft down to negative frequency at special q points under different critical strains, i.e., epsilon_a = 11.55 percent along a-axis (with W-W chains) direction, epsilon_b = 7.0 percent along b-axis direction…
Regulation of electronic structure and mobility cut-on rate in two-dimensional transition metal dichalcogenides (TMDs) has attracted much attention because of its potential in electronic device design. The anisotropic Raman scattering and mobility cut-on rate of monolayer unique distorted-1T(1Td) ReS2 with external strain are determined theoretically based on the density function theory. The angle-dependent Raman spectrum of Ag-like, Eg-like and Cp models are used to discriminate and analysis structural anisotropy; the strain is exploited to adjust the structural symmetry and electronic struct…
Strain is prominent in fabricated samples of two-dimensional semiconductors and it also serves as an exploitable tool for engineering their properties. However, quantifying strain and characterizing its spatially inhomogeneous distribution across a material are challenging tasks. Here, we report the lattice vibrational modes and corresponding Raman spectra of strained monolayer black phosphorus (phosphorene) by first-principles simulations. We show that frequencies of vibrational modes of phosphorene and their Raman scattering peaks exhibit substantial and distinct shifts according to the type…
By performing density functional theory-based ab-initio calculations, Raman active phonon modes of novel single-layer two-dimensional (2D) materials and the effect of in-plane biaxial strain on the peak frequencies and corresponding activities of the Raman active modes are calculated. Our findings confirm the Raman spectrum of the unstrained 2D crystals and provide expected variations in the Raman active modes of the crystals under in-plane biaxial strain. The results are summarized as follows; (i) frequencies of the phonon modes soften (harden) under applied tensile (compressive) strains, (ii…
Experimental demonstrations of 1D van der Waals material tellurium have been presented by Raman spectroscopy under strain and magneto-transport. Raman spectroscopy measurements have been performed under strains along different principle axes. Pronounced strain response along c-axis is observed due to the strong intra-chain covalent bonds, while no strain response is obtained along a-axis due to the weak inter-chain van der Waals interaction. Magneto-transport results further verify its anisotropic property, resulting in dramatically distinct magneto-resistance behaviors in terms of three diffe…
Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q = 0) wave-vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene (1LG) in the frequency range from 2350 to 2750 cm-1, which shows the G* and the G'-band features originating from a double-resonant Raman process with q \not= 0. The observed phonon renormalization effects are different from what is observed for the zone-center q = 0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons…
Under homogeneous uniaxial strains, the Raman 2D band of graphene involving two-phonon double-resonance scattering processes splits into two peaks and they altogether redshift strongly depending on the direction and magnitude of the strain. Through polarized micro- Raman measurements and first-principles calculations, the effects are shown to originate from significant changes in resonant conditions owing to both the distorted Dirac cones and anisotropic modifications of phonon dispersion under uniaxial strains. Quantitative agreements between the calculation and experiment enable us to determ…
The polarization dependences of the G, D, and 2D (G$'$) bands in Raman spectra at graphene bulk and edge are examined theoretically. The 2D and D bands have different selection rules at bulk and edge. At bulk, the 2D band intensity is maximum when the polarization of the scattered light is parallel to that of incident light, whereas the D band intensity does not have a polarization dependence. At edge, the 2D and D bands exhibit a selection rule similar to that of the G band proposed in a previous paper. We suggest that a constraint equation on the axial velocity caused by the graphene edge is…
We study the 2D Raman band of in-plane uniaxially strained graphene within a non-orthogonal tight-binding model. At non-zero strain, the obtained 2D band splits into two subbands at strain angles $0^{\circ}$ and $30^{\circ}$ or into three subbands at intermediate angles. The evolution of the 2D subbands is calculated systematically in the range of the accessible strains from -1% to 3% and for the commonly used laser photon energy from 1.5 eV to 3.0 eV. The strain rate and dispersion rate of the 2D subbands are derived and tabulated. In particular, these two quantities show large variations up …
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.
A new type of two-dimensional layered semiconductor with weak electrostatic but not van der Waals interlayer interactions, Bi2O2Se, has been recently synthesized, which shown excellent air stability and ultrahigh carrier mobility. Herein, we combined theoretical and experimental approaches to study the Raman spectra of Bi2O2Se and related bismuth oxychalcogenides (Bi2O2Te and Bi2O2S). The experimental peaks were fully consistent with the calculated results, and were successfully assigned. Bi2O2S was predicted to have more Raman-active modes due to its lower symmetry. The shift of the predicted…
The vibrational and electronic properties of 2-dimensinal (2D) materials can be efficiently tuned by external strain due to their good stretchability. Resonant Raman spectroscopy is a versatile tool to study the physics of phonons, electrons and their interactions simultaneously, which is particularly useful for the investigation of strain effect on 2D materials. Here, for the first time, we report the resonant Raman study of strained few-layer InSe (γ-phase). Under ~ 1% of uniaxial tensile strain, one order of magnitude enhancement of Raman intensity for longitudinal optical (LO) phonon is ob…
We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of $10^{-4}$, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy \textit{in situ} provide…
Confocal Raman spectroscopy is a versatile, non-invasive investigation tool and a major workhorse for graphene characterization. Here we show that the experimentally observed Raman 2D line width is a measure of nanometer-scale strain variations in graphene. By investigating the relation between the G and 2D line at high magnetic fields we find that the 2D line width contains valuable information on nanometer-scale flatness and lattice deformations of graphene, making it a good quantity for classifying the structural quality of graphene even at zero magnetic field.
Core-shell Ge-SixGe1-x nanowires (NWs) are expected to contain large strain fields due to the lattice-mismatch at the core/shell interface. Here we report the measurement of core strain in a NW heterostructure using Raman spectroscopy. We compare the Raman spectra, and the frequency of the Ge-Ge mode measured in individual Ge-Si0.5Ge0.5 core-shell, and bare Ge NWs. We find that the Ge-Ge mode frequency is diameter-independent in GeNWs with a value similar to that of bulk Ge, 300.5 cm-1. On the other hand, Ge-Si0.5Ge0.5 core-shell nanowires reveal a strain-induced blue shift of the Ge-Ge mode, …
Polarization dependent Raman scattering experiments realized on single GaAs nanowires with different percentages of zinc-blende and wurtzite structure are presented. The selection rules for the special case of nanowires are found and discussed. In the case of zinc-blende, the transversal optical mode E1(TO) at 267 cm-1 exhibits the highest intensity when the incident and analyzed polarization are parallel to the nanowire axis. This is a consequence of the nanowire geometry and dielectric mismatch with the environment, and in quite good agreement with the Raman selection rules. We also find a c…
Herein we report experimental evidence of directional SERS from molecules situated inside a single nanowire-nanoparticle junction cavity. The emission was confined to a narrow range of wavevectors perpendicular to the axis of the cavity. In addition to this, the molecules excite multiple guided modes of the nanowire which were imaged using leakage radiation Fourier microscopy. We further characterize the emission wavevectors as a function of output polarization. The excited guided modes of the wire show interesting polarization signatures. All the results were corroborated using finite element…
The Young's modulus of graphene is estimated by measuring the strain applied by a pressure difference across graphene membranes using Raman spectroscopy. The strain induced on pressurized graphene balloons can be estimated directly from the peak shift of the Raman G band. By comparing the measured strain with numerical simulation, we obtained the Young's modulus of graphene. The estimated Young's modulus values of single- and bi-layer graphene are 2.4\pm0.4 TPa and 2.0\pm0.5 TPa, respectively.
We have carried out Raman spectroscopy experiments to investigate two-magnon excitations in epitaxial thin films of the quasi-two-dimensional antiferromagnetic Mott insulator Sr$_2$IrO$_4$ under in-plane misfit strain. With in-plane biaxial compression, the energy of the two-magnon peak increases, and the peak remains observable over a wider temperature range above the Néel temperature, indicating strain-induced enhancement of the superexchange interactions between $\it{J}_{eff}$ = 1/2 pseudospins. From density functional theory calculations, we have found an increase of the nearest-neighbor h…
Strained trigonal Te has been predicted to host Weyl nodes supported by a non-symmorphic chiral symmetry. Using low-pressure physical vapor deposition, we systematically explored the growth of trigonal Te nanowires with naturally occurring strain caused by curvature of the wires. Raman spectra and high mobility electronic transport attest to the highly crystalline nature of the wires. Comparison of Raman spectra for both straight and curved nanowires indicates a breathing mode that is significantly broader and shifted in frequency for the curved wires. Strain induced by curvature during growth…
We present an in-depth analysis of the electronic and vibrational band structure of uniaxially strained graphene by ab-initio calculations. Depending on the direction and amount of strain, the Fermi crossing moves away from the $K$-point. However, graphene remains semimetallic under small strains. The deformation of the Dirac cone near the $K$-point gives rise to a broadening of the 2D Raman mode. In spite of specific changes in the electronic and vibrational band structure the strain-induced frequency shifts of the Raman active E2g and 2D modes are independent of the direction of strain. Thus…
We present low-temperature Raman measurements on gate tunable graphene encapsulated in hexagonal boron nitride, which allows to study in detail the Raman G and 2D mode frequencies and line widths as function of the charge carrier density. We observe a clear softening of the Raman G mode (of up to 2.5 cm$^{-1}$) at low carrier density due to the phonon anomaly and a residual G~mode line width of $\approx$ 3.5 cm$^{-1}$ at high doping. From analyzing the G mode dependence on doping and laser power we extract an electron-phonon-coupling constant of $\approx$ 4.4 $\times$ 10$^{-3}$ (for the G mode…
We use micro-Raman and photoluminescence (PL) spectroscopy at 300K to investigate the influence of uniaxial tensile strain on the vibrational and optoelectronic properties of monolayer and bilayer MoS2 on a flexible substrate. The initially degenerate E^1_{2g} Raman mode is split into a doublet as a direct consequence of the strain applied to MoS2 through Van der Waals coupling at the sample-substrate interface. We observe a strong shift of the direct band gap of 48meV/(% of strain) for the monolayer and 46meV/% for the bilayer, whose indirect gap shifts by 86meV/%. We find a strong decrease o…
Bi-layer graphene with a twist angle θ between the layers generates a superlattice structure known as Moiré pattern. This superlattice provides a θ-dependent q wavevector that activates phonons in the interior of the Brillouin zone. Here we show that this superlattice-induced Raman scattering can be used to probe the phonon dispersion in twisted bi-layer graphene (tBLG). The effect reported here is different from the broadly studied double-resonance in graphene-related materials in many aspects, and despite the absence of stacking order in tBLG, layer breathing vibrations (namely ZO' phonons) …
We use confocal Raman microscopy and modified vector analysis methods to investigate the nanoscale origin of strain and carrier concentration in exfoliated graphene-hexagonal boron nitride (hBN) heterostructures on silicon dioxide (SiO2). Two types of heterostructures are studied: graphene on SiO2 partially coved by hBN, and graphene fully encapsulated between two hBN flakes. We extend the vector analysis methods to produce spatial maps of the strain and doping variation across the heterostructures. This allows us to visualise and directly quantify the much-speculated effect of the environment…
We study the dependence of the plasmon dispersion relation of graphene on applied uniaxial strain. Besides electron correlation at the RPA level, we also include local field effects specific for the honeycomb lattice. As a consequence of the two-band character of the electronic band structure, we find two distinct plasmon branches. We recover the square-root behavior of the low-energy branch, and find a nonmonotonic dependence of the strain-induced modification of its stiffness, as a function of the wavevector orientation with respect to applied strain.
New techniques for probing hyperbolic phonon polaritons (HPP) in 2D materials will support the development of the emerging technologies in this field. Previous reports have shown that it is possible for WSe2 monolayers in contact with the hexagonal boron nitride (hBN) to generate HPP in the hBN via Raman scattering. In this paper, we set out new results on HPP Raman scattering induced in hBN by WSe2 and MoSe2 monolayers including new resonances at which the Raman scattering is enhanced. Analysis of the observed Raman lineshapes demonstrates that Raman scattering allows HPP with wavevectors wit…
We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45T. This reveals a filling-factor-dependent, multi-component anticrossing structure of the Raman G peak, resulting from magnetophonon resonances between magnetoexcitons and E$_{2g}$ phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier densities and strain. Random fluctuations of strain-induced pseudo-magnetic fields lead to increased scattering intensity inside the anti-crossing gap, consistent with the experiment.
The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically-exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the …
We report on a scanning confocal Raman spectroscopy study investigating the strain-uniformity and the overall strain and doping of high-quality chemical vapour deposited (CVD) graphene-based heterostuctures on a large number of different substrate materials, including hexagonal boron nitride (hBN), transition metal dichalcogenides, silicon, different oxides and nitrides, as well as polymers. By applying a hBN-assisted, contamination free, dry transfer process for CVD graphene, high-quality heterostructures with low doping densities and low strain variations are assembled. The Raman spectra of …
We experimentally demonstrate that the Raman active optical phonon modes of single layer graphene can be modulated by the dynamic local strain created by surface acoustic waves (SAWs). In particular, the dynamic strain field of the SAW is shown to induce a Raman scattering intensity variation as large as 15% and a phonon frequency shift of up to 10 cm$^{-1}$ for the G band, for instance, for an effective hydrostatic strain of 0.24% generated in a single layer graphene atop a LiNbO$_{3}$ piezoelectric substrate with a SAW resonator operating at a frequency of $ \sim $ 400 MHz. Thus, we demonstr…
Since lattice strain and charge density affect various material properties of graphene, a reliable and efficient method is required for quantification of the two variables. While Raman spectroscopy is sensitive and non-destructive, its validity towards precise quantification of chemical charge doping has not been tested. In this work, we quantified in-situ the fractional frequency change of 2D and G peaks in response of charge density induced by sulfuric acid solution as well as native lattice strain. Based on the experimental data and theoretical corroboration, we presented an optical method …
The modification of single layer graphene due to intense, picoseconds near-infrared laser pulses is investigated. We monitor the stable changes introduced to graphene upon photoexcitation using Raman spectroscopy. We find that photoexcitation leads to both a local increase in hole doping and a reduction in compressive strain. Possible explanations for these effects, due to photo-induced oxygenation and photo-induced buckling of the graphene, are discussed.
We report a first-principles study on the elastic, vibrational, and electronic properties of recently synthesized phosphorene. By calculating Grüneisen parameters, we evaluate the frequency shift of Raman/infrared active modes via symmetric biaxial strain. We also study an inducing semiconductor-metal transition, the gap size, and effective mass of carriers in various strain configurations. Furthermore, we unfold the emergence of a peculiar Dirac-shaped dispersion for specific strain conditions, including the zigzag-oriented tensile strain. The observed linear energy spectrum has distinct velo…
We derive the frequency shifts and the broadening of $Γ$ point longitudinal optical (LO) and transverse optical (TO) phonon modes, due to electron-phonon interaction, in graphene under uniaxial strain as a function of the electron density and the disorder amount. We show that, in the absence of a shear strain component, such interaction gives rise to a lifting of the degeneracy of the LO and TO modes which contributes to the splitting of the G Raman band. The anisotropy of the electronic spectrum, induced by the strain, results in a polarization dependence of the LO and TO modes. This dependen…
An analytical study is presented of the double resonant Raman scattering process in graphene, responsible for the D and D$^{\prime}$ features in the Raman spectra. This work yields analytical expressions for the D and D$^{\prime}$ integrated Raman intensities that explicitly show the dependencies on laser energy, defect concentration, and electronic lifetime. Good agreement is obtained between the analytical results and experimental measurements on samples with increasing defect concentrations and at various laser excitation energies. The use of Raman spectroscopy to identify the nature of def…
Intervalley scattering of carriers in graphene at `top' adatoms may give rise to a hidden Kekulé ordering pattern in the adatom positions. This ordering is the result of a rapid modulation in the electron-mediated interaction between adatoms at the wavevector $K- K'$, which has been shown experimentally and theoretically to dominate their spatial distribution. Here we show that the adatom interaction is extremely sensitive to strain in the supporting graphene, which leads to a characteristic spatial modulation of the Kekulé order as a function of adatom distance. Our results suggest that the s…
We present a systematic experimental and theoretical study of the two-phonon (2D) Raman scattering in graphene under uniaxial tension. The external perturbation unveils that the 2D mode excited with 785nm has a complex line-shape mainly due to the contribution of two distinct double resonance scattering processes (inner and outer) in the Raman signal. The splitting depends on the direction of the applied strain and the polarization of the incident light. The results give new insight into the nature of the 2D band and have significant implications for the use of graphene as reinforcement in com…
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…
We report a comprehensive study of the two-phonon inter-valley (2D) Raman mode in graphene monolayers, motivated by recent reports of asymmetric 2D-mode lineshapes in freestanding graphene. For photon energies in the range $1.53 \rm eV - 2.71 \rm eV$, the 2D-mode Raman response of freestanding samples appears as bimodal, in stark contrast with the Lorentzian approximation that is commonly used for supported monolayers. The transition between the freestanding and supported cases is mimicked by electrostatically doping freestanding graphene at carrier densities above $2\times 10^{11} \rm cm^{-2}…
A constant height of gallium nitride (GaN) nanowires with graphene deposited on them is shown to have a strong enhancement of Raman scattering, whilst variable height nanowires fail to give such an enhancement. Scanning electron microscopy reveals a smooth graphene surface which is present when the GaN nanowires are uniform, whereas graphene on nanowires with substantial height differences is observed to be pierced and stretched by the uppermost nanowires. The energy shifts of the characteristic Raman bands confirms that these differences in the nanowire height has a significant impact on the …
We have performed systematic investigations of transport through graphene on hexagonal boron nitride (hBN) substrates, together with confocal Raman measurements and a targeted theoretical analysis, to identify the dominant source of disorder in this system. Low-temperature transport measurements on many devices reveal a clear correlation between the carrier mobility $μ$ and the width $n^*$ of the resistance peak around charge neutrality, demonstrating that charge scattering and density inhomogeneities originate from the same microscopic mechanism. The study of weak-localization unambiguously s…
We report a combined electron transmission and Raman spectroscopy study of InAs nanowires. We demonstrate that the temperature dependent behavior of optical phonon energies can be used to determine the relative wurtzite fraction in the InAs nanowires. Furthermore, we propose that the interfacial strain between zincblende and wurtzite phases along the length of the wires manifests in the temperature-evolution of the phonon linewidths. From these studies, temperature-dependent Raman measurements emerge has a non-invasive method to study polytypism in such nanowires.
Hyperbolic crystals like α-MoO$_3$ can support large wavevectors and photon density as compared to the commonly used dielectric crystals, which makes them a highly desirable platform for compact photonic devices. The extreme anisotropy of the dielectric constant in these crystals is intricately linked with the anisotropic character of the phonons, which along with photon confinement leads to the rich physics of phonon polaritons. However, the chiral nature of phonons in these hyperbolic crystals have not been studied in detail. In this study, we report our observations of helicity selective Ra…
It is important to study the van der Waals interface in emerging vertical heterostructures based on layered two-dimensional (2D) materials. Being atomically thin, 2D materials are susceptible to significant strains as well as charge transfer doping across the interfaces. Here we use Raman and photoluminescence (PL) spectroscopy to study the interface between monolayer graphene/MoS2 heterostructures prepared by mechanical exfoliation and layer-by-layer transfer. By using correlation analysis between the Raman modes of graphene and MoS2 we show that both layers are subjected to compressive strai…
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…
The recent emergence of strain gradient engineering directly affects the nanomechanics, optoelectronics and thermal transport fields in 2D materials. More specifically, large suspended graphene under very high stress represents the quintessence for nanomechanical mass detection through unique molecular reactions. Different techniques have been used to induce strain in 2D materials, for instance by applying tip indentation, pressure or substrate bending on a graphene membrane. Nevertheless, an efficient way to control the strain of a structure is to engineer the system geometry as shown in ever…
We present detailed Raman studies of graphene deposited on gallium nitride nanowires with different variations in height. Our results show that different density and height of nanowires being in contact with graphene impact graphene properties like roughness, strain and carrier concentration as well as density and type of induced defects. Detailed analysis of Raman spectra of graphene deposited on different nanowire substrates shows that bigger differences in nanowires height increase graphene strain, while higher number of nanowires in contact with graphene locally reduce the strain. Moreover…
We present a thermal annealing study on single-layer and bilayer (BLG) graphene encapsulated in hexagonal boron nitride. The samples are characterized by electron transport and Raman spectroscopy measurements before and after each annealing step. While extracted material properties such as charge carrier mobility, overall doping, and strain are not influenced by the annealing, an initial annealing step lowers doping and strain variations and thus results in a more homogeneous sample. Additionally, the narrow 2D-sub-peak widths of the Raman spectrum of BLG, allow us to extract information about…
