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) the response of the Raman activities to applied strain for the in-plane and out-of-plane vibrational modes have opposite trends, thus, the built-in strains in the materials can be monitored by tracking the relative activities of those modes, (iii) in particular, the A-peak in single-layer Si and Ge disappear under a critical tensile strain, (iv) especially in mono and di- atomic single-layers, the shift of the peak frequencies is stronger indication of the strain rather than the change in Raman activities, (v) Raman active modes of single-layer ReX 2 (X=S, Se) are almost irresponsive to the applied strain. Strain-induced modifications in the Raman spectrum of 2D materials in terms of the peak positions and the relative Raman activities of the modes could be a convenient tool for characterization.
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…
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…
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, …
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 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…
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…
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…
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…
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.
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 …
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…
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…
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 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…
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.
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…
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…
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…
The Raman 2D line of graphene is widely used for device characterization and during device fabrication as it contains valuable information on e.g. the direction and magnitude of mechanical strain and doping. Here we present systematic asymmetries in the 2D line shape of exfoliated graphene and graphene grown by chemical vapor deposition. Both graphene crystals are fully encapsulated in van der Waals heterostructures, where hexagonal boron nitride and tungsten diselenide are used as substrate materials. In both material stacks, we find very low doping values and extremely homogeneous strain dis…
We report a comprehensive micro-Raman study of a pressurized suspended graphene membrane that hermetically seals a circular pit, etched in a Si/SiO$_2$ substrate. Placing the sample under a uniform pressure load results in bulging of the graphene membrane and subsequent softening of the main Raman features, due to tensile strain. In such a microcavity, the intensity of the Raman features depends very sensitively on the distance between the graphene membrane and the Si substrate, which acts as the bottom mirror of the cavity. Thus, a spatially resolved analysis of the intensity of the G- and 2D…
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…
We present a comprehensive study of graphene grown by chemical vapor deposition on copper single crystals with exposed (100), (110) and (111) faces. Direct examination of the as-grown graphene by Raman spectroscopy using a range of visible excitation energies and microRaman mapping shows distinct strain and doping levels for individual Cu surfaces. Comparison of results from Raman mapping with X-ray diffraction techniques and Atomic Force Microscopy shows it is neither the crystal quality nor the surface topography responsible for the specific strain and doping values, but it is the Cu lattice…
Strain engineering is widely used in material science to tune the (opto-)electronic properties of materials and enhance the performance of devices. Two-dimensional atomic crystals are a versatile playground to study the influence of strain, as they can sustain very large deformations without breaking. Various optical techniques have been employed to probe strain in two-dimensional materials, including micro-Raman and photoluminescence spectroscopy. Here we demonstrate that optical second harmonic generation constitutes an even more powerful technique, as it allows to extract the full strain te…
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…
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…
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 …
Electronic localization and optical activity of strain-engineered transition-metal dichalcogenide nanobubbles
Institute of Physics, Carl von Ossietzky Universität Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学物理研究所）；Friedrich-Schiller Universität Jena, Institute for Condensed Matter Theory and Optics（耶拿弗里德里希·席勒大学凝聚态理论与光学研究所）；Center for Nanoscale Dynamics (CeNaD), Carl von Ossietzky Universität Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学纳米动力学中心）
We demonstrate a method to induce tensile and compressive strain into two-dimensional transition metal dichalcogenide (TMDC) MoS$_{2}$ via the deposition of stressed thin films to encapsulate exfoliated flakes. With this technique we can directly engineer MoS$_{2}$ strain magnitude by changing deposited thin film stress, therefore allowing variable strain to be applied on a flake-to-flake level. These thin film stressors are analogous to SiN$_{x}$ based stressors implemented in industrial CMOS processes to enhance Si mobility, suggesting that our concept is highly scalable and may be applied f…
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 …
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.
The controlled tunability of superconductivity in low-dimensional materials may enable new quantum devices. Particularly in triplet or topological superconductors, tunneling devices such as Josephson junctions etc. can demonstrate exotic functionalities. The tunnel barrier, an insulating or normal material layer separating two superconductors, is a key component for the junctions. Thin layers of NbSe2 have been shown as a superconductor with strong spin orbit coupling, which can give rise to topological superconductivity if driven by a large magnetic exchange field. Here we demonstrate the sup…
Graphene, due to its superior stretchability, exhibits rich structural deformation behaviors and its strain-engineering has proven useful in modifying its electronic and magnetic properties. Despite the strain-sensitivity of the Raman G and 2D modes, the optical characterization of the native strain in graphene on silica substrates has been hampered by excess charges interfering with both modes. Here we show that the effects of strain and charges can be optically separated from each other by correlation analysis of the two modes, enabling simple quantification of both. Graphene with in-plane s…
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…
