Layer Breathing Modes Research Articles

Ultralow-Frequency Tip-Enhanced Raman Scattering Discovers Nanoscale Radial Breathing Mode on Strained 2D Semiconductors.

Collective excitations including plasmons, magnons, and layer-breathing vibration modes emerge at an ultralow frequency (<1 THz) and are crucial for understanding van der Waals materials. Strain at the nanoscale can drastically change the property of van der Waals materials and create localized states like quantum emitters. However, it remains unclear how nanoscale strain changes collective excitations. Herein, ultralow-frequency tip-enhanced Raman spectroscopy (TERS) with sub-10nm resolution under ambient conditions is developed to explore the localized collective excitation on monolayer semiconductors with nanoscale strains. A new vibrational mode is discovered at around 12 cm-1 (0.36 THz) on monolayer MoSe2 nanobubbles and it is identified as the radial breathing mode (RBM) of the curved monolayer. The correlation is determined between the RBM frequency and the strain by simultaneously performing deterministic nanoindentation and TERS measurement on monolayer MoSe2. The generality of the RBM in nanoscale curved monolayer WSe2 and bilayer MoSe2 is demonstrated. Using the RBM frequency, the strain of the monolayer MoSe2 on the nanoscale can be mapped. Such an ultralow-frequency vibration from curved van der Waals materials provides a new approach to study nanoscale strains and points to more localized collective excitations to be discovered at the nanoscale.

Determining by Raman spectroscopy the average thickness and N-layer-specific surface coverages of MoS2 thin films with domains much smaller than the laser spot size.

Raman spectroscopy is a widely used technique to characterize nanomaterials because of its convenience, non-destructiveness, and sensitivity to materials change. The primary purpose of this work is to determine via Raman spectroscopy the average thickness of MoS2 thin films synthesized by direct liquid injection pulsed-pressure chemical vapor deposition (DLI-PP-CVD). Such samples are constituted of nanoflakes (with a lateral size of typically 50 nm, i.e., well below the laser spot size), with possibly a distribution of thicknesses and twist angles between stacked layers. As an essential preliminary, we first reassess the applicability of different Raman criteria to determine the thicknesses (or layer number, N) of MoS2 flakes from measurements performed on reference samples, namely well-characterized mechanically exfoliated or standard chemical vapor deposition MoS2 large flakes deposited on 90 ± 6 nm SiO2 on Si substrates. Then, we discuss the applicability of the same criteria for significantly different DLI-PP-CVD MoS2 samples with average thicknesses ranging from sub-monolayer up to three layers. Finally, an original procedure based on the measurement of the intensity of the layer breathing modes is proposed to evaluate the surface coverage for each N (i.e., the ratio between the surface covered by exactly N layers and the total surface) in DLI-PP-CVD MoS2 samples.

Twist Angle-Dependent Intervalley Charge Carrier Transfer and Recombination in Bilayer WS2.

A twist angle at a van der Waals junction provides a handle to tune its optoelectronic properties for a variety of applications, and a comprehensive understanding of how the twist modulates electronic structure, interlayer coupling, and carrier dynamics is needed. We employ time-dependent density functional theory and nonadiabatic molecular dynamics to elucidate angle-dependent intervalley carrier transfer and recombination in bilayer WS2. Repulsion between S atoms in twisted configurations weakens interlayer coupling, increases the interlayer distance, and softens layer breathing modes. Twisting has a minor influence on K valleys while it lowers Γ valleys and raises Q valleys because their wave functions are delocalized between layers. Consequently, the reduced energy gaps between the K and Γ valleys accelerate the hole transfer in the twisted structures. Intervalley electron transfer proceeds nearly an order of magnitude faster than hole transfer. The more localized wave functions at K than Q values and larger bandgaps result in smaller nonadiabatic couplings for intervalley recombination, making it 3-4 times slower in twisted than high-symmetry structures. B2g breathing, E2g in-plane, and A1g out-of-plane modes are most active during intervalley carrier transfer and recombination. The faster intervalley transfer and extended carrier lifetimes in twisted junctions are favorable for optoelectronic device performance.

Anomalous interlayer vibrations in few-layer InSe induced by weak intralayer bonding

Atomically thin InSe is a promising semiconductor that possesses exceptional plasticity, high electron mobility, and wide bandgap tunability, which are thought to be highly sensitive to interlayer coupling. Since the interlayer vibration modes can provide direct access to the interlayer coupling strength, in this study, we systematically investigated the interlayer modes in few-layer InSe using low-frequency Raman spectroscopy. We found that the commonly used linear chain model (LCM), which treats the single layer as a rigid entity, is inadequate in accurately describing the frequencies of interlayer shear modes in InSe due to the influence of weak in-plane intralayer In–In bonding. This issue can be addressed with a modified model that accounts for both the in-plane interlayer coupling between InSe layers and the in-plane intralayer interaction within InSe layers. However, the out-of-plane intralayer In–In bonding is strong enough so that it has negligible impact on the frequency of the interlayer layer-breathing modes, which can be well understood by the LCM. Our study reveals how the weak intralayer bonding in two-dimensional materials gives a non-negligible contribution to the corresponding interlayer vibrations.

Enhanced Layer-Breathing Modes in van der Waals Heterostructures Based on Twisted Bilayer Graphene.

The characterization of interlayer coupling in two-dimensional van der Waals heterostructures (vdWHs) is essential to understand their quantum behaviors and structural functionalities. Interlayer shear and layer-breathing (LB) phonons carry rich information on interlayer interaction, but they are usually too weak to be detected via standard Raman spectroscopy due to the weak electron-phonon coupling (EPC). Here, we report a universal strategy to enhance LB modes of vdWHs based on twisted bilayer graphene (tBLG). In both tBLG/hBN and tBLG/MoS2 vdWHs, the resonantly excited electrons in tBLG can strongly couple to LB phonons extended over the entire layers in the vdWHs, whose resonance condition is tunable by the twist angle of tBLG. In vdWHs containing twisted graphene layers with multiple twisted interfaces, the EPC of LB phonons coming from the collective LB vibrations of entire heterostructure layers can be tuned by resonant excitation of programmable van Hove singularities according to each twisted interface. The universality and tunability of enhanced LB phonons by tBLG make it a promising method to investigate EPC and interlayer interaction in related vdWHs.

Low-energy moiré phonons in twisted bilayer van der Waals heterostructures

We develop a low-energy continuum model for phonons in twisted moir\'e bilayers, based on a configuration-space approach. In this approach, interatomic force constants are obtained from density functional theory (DFT) calculations of untwisted bilayers with various in-plane shifts. This allows for efficient computation of phonon properties for any small twist angle, while maintaining DFT-level accuracy. Based on this framework, we show how the low-energy phonon modes, including interlayer shearing and layer-breathing modes, vary with the twist angle. As the twist angle decreases, the frequencies of the low-energy modes are reordered and the atomic displacement fields corresponding to phonon eigenmodes break translational symmetry, developing periodicity on the moir\'e length scale. We demonstrate the capabilities of our model by calculating the phonon properties of three specific structures: bilayer graphene, bilayer molybdenum disulfide (MoS$_2$), and molybdenum diselenide-tungsten diselenide (MoSe$_2$-WSe$_2$).

Observation of Strong Interlayer Couplings in WS2/MoS2 Heterostructures via Low-Frequency Raman Spectroscopy.

Van der Waals (vdW) heterostructures based on two-dimensional (2D) transition metal dichalcogenides (TMDCs), particularly WS2/MoS2 heterostructures with type-II band alignments, are considered as ideal candidates for future functional optoelectronic applications owing to their efficient exciton dissociation and fast charge transfers. These physical properties of vdW heterostructures are mainly influenced by the interlayer coupling occurring at the interface. However, a comprehensive understanding of the interlayer coupling in vdW heterostructures is still lacking. Here, we present a detailed analysis of the low-frequency (LF) Raman modes, which are sensitive to interlayer coupling, in bilayers of MoS2, WS2, and WS2/MoS2 heterostructures directly grown using chemical vapor deposition to avoid undesirable interfacial contamination and stacking mismatch effects between the monolayers. We clearly observe two distinguishable LF Raman modes, the interlayer in-plane shear and out-of-plane layer-breathing modes, which are dependent on the twisting angles and interface quality between the monolayers, in all the 2D bilayered structures, including the vdW heterostructure. In contrast, LF modes are not observed in the MoS2 and WS2 monolayers. These results indicate that our directly grown 2D bilayered TMDCs with a favorable stacking configuration and high-quality interface can induce strong interlayer couplings, leading to LF Raman modes.

Molecular beam epitaxy of PtSe2 using a co-deposition approach

The structural properties of co-deposited ultrathin PtSe2 films grown at low temperatures by molecular beam epitaxy on c-plane Al2O3 are studied. By simultaneously supplying a Se flux from a Knudsen cell and Pt atoms from an electron-beam evaporator, crystalline (001)-oriented PtSe2 films were formed between 200 °C and 300 °C. The long separation between substrate and electron beam evaporator of about 60 cm ensured minimal thermal load. At optimum deposition temperatures, a ten times or even higher supply rate of Se compared to Pt ensured that the pronounced volatility of the Se was compensated and the PtSe2 phase was formed and stabilized at the growth front. Postgrowth anneals under a Se flux was found to dramatically improve the crystalline quality of the films. Even before the postgrowth anneal in Se, the crystallinity of PtSe2 films grown with the co-deposition method was superior to films realized by thermal assisted conversion. Postgrowth annealed films showed Raman modes with narrower peaks and more than twice the intensity. Transmission electron microscopy investigations revealed that the deposited material transitioned to a two-dimensional layered structure only after the postgrowth anneal. PtSe2 growth was found to start as single layer islands that preferentially nucleated at atomic steps of the substrate and progressed in a layer-by-layer like fashion. A close to ideal wetting behavior resulted in coalesced PtSe2 films after depositing about 1.5 PtSe2 layers. Detailed Raman investigation of the observed PtSe2 layer breathing modes of films grown under optimized co-deposition conditions revealed an interlayer coupling force constant of 5.0–5.6 × 1019 N m−3.

Shear and Breathing Modes of Layered Materials.

Layered materials (LMs), such as graphite, hexagonal boron nitride, and transition-metal dichalcogenides, are at the center of an ever-increasing research effort, due to their scientific and technological relevance. Raman and infrared spectroscopies are accurate, non-destructive approaches to determine a wide range of properties, including the number of layers, N, and the strength of the interlayer interactions. We present a general approach to predict the complete spectroscopic fan diagrams, i.e., the relations between frequencies and N for the optically active shear and layer-breathing modes of any multilayer comprising N ≥ 2 identical layers. In order to achieve this, we combine a description of the normal modes in terms of a one-dimensional mechanical model, with symmetry arguments that describe the evolution of the point group as a function of N. Group theory is then used to identify which modes are Raman- and/or infrared-active, and to provide diagrams of the optically active modes for any stack composed of identical layers. We implement the method and algorithms in an open-source tool to assist researchers in the prediction and interpretation of such diagrams. Our work will underpin future efforts on Raman and infrared characterization of known, and yet not investigated, LMs.

Operando Measurement of Layer Breathing Modes in Lithiated Graphite

Despite their ubiquitous usage and increasing societal dependence on Li-ion batteries, there remains a lack of detailed empirical evidence of Li intercalation/deintercalation into graphite even though this process dictates the performance, longevity, and safety of the system. Here, we report direct detection and dissociation of specific crystallographic phases in the lithiated graphite, which form through a stepwise staging process. Using operando measurements, LiC18, LiC12, and LiC6 phases are observed via distinct low-frequency Raman features, which are the result of displacement of the graphite lattice by induced local strain. Density functional theory calculations confirm the nature of the Raman-active vibrational modes, to the layer breathing modes (LBMs) of the lithiated graphite. The new findings indicate graphene-like characteristics in the lithiated graphite under the deep charged condition due to the imposed strain by the inserted Li. Moreover, our approach also provides a simple experimental tool to measure induced strain in the graphite structure under full intercalation conditions.

Temperature dependent Raman spectroscopy of shear and layer breathing modes in bilayer MoS2

We report low-frequency Raman scattering results of bilayer (2L) MoS2 structures with 3R and 2H stacking orders. The stacking orders were identified by Raman mapping images of the low-frequency shear (S) and layer breathing (B) modes. Linear temperature coefficients (χ) were obtained from temperature-dependent frequency changes of the shear and layer breathing modes for the 3R- and 2H-stacked 2L MoS2: χ3RS=−0.011±0.006cm−1/K, χ2HS=−0.009±0.002cm−1/K, χ3RB=−0.009±0.003cm−1/K, and χ2HB=−0.010±0.002cm−1/K. Interestingly, the temperature coefficients were significantly reduced after the MoS2 samples were thermally heated: χ3RS=−0.004±0.001cm−1/K, χ2HS=−0.004±0.001cm−1/K, χ3RB=−0.002±0.001cm−1/K, and χ2HB=−0.002±0.001cm−1/K. Similar behaviors were also observed for the temperature coefficients of the high-frequency E2g1 and A1g phonons. The heating-induced modifications in the temperature coefficients are attributed to changes in the MoS2–substrate coupling. Our result further paves the way for optimal design strategies for low-dimensional device applications where thermal management plays a crucial role in device performance.

Structural configurations and Raman spectra of carbon nanoscrolls

Three types of carbon nanoscroll (CNS) structures that are formed when scrolling up graphene sheets are investigated using Raman spectroscopy and atomic force microscopy (AFM). The CNSs were produced from exfoliated monolayer graphene deposited on a Si chip by applying a droplet of isopropyl alcohol (IPA) solution. The three types of CNS are classified as single-elliptical-core, double-elliptical-core (both with large internal volumes) and collapsed ribbon-like, based on AFM surface profile measurements. We discuss the structure and formation of CNS with much larger hollow cores than is commonly assumed and relate this to the large effective 2D bending stiffness of graphene in the IPA solution. The large elliptical core structures show Raman spectra similar to those previously reported for CNS and indicate little interaction between the scrolled layers. The Raman spectra from ribbon-like structures show additional features that are similar to that of folded graphene. These new features can be related to layer breathing modes combined with some resonance enhancement at specific regions of the ribbon-like CNSs that are due to specific twist angles produced when the structure folds/collapses.

Phonons in twisted transition-metal dichalcogenide bilayers: Ultrasoft phasons and a transition from a superlubric to a pinned phase

The tunability of the interlayer coupling by twisting one layer with respect to another layer of two-dimensional materials provides a unique way to manipulate the phonons and related properties. We refer to this engineering of phononic properties as "Twistnonics". We study the effects of twisting on low-frequency shear (SM) and layer breathing (LBM) modes in transition metal dichalcogenide (TMD) bilayer using atomistic classical simulations. We show that these low-frequency modes are extremely sensitive to twist and can be used to infer the twist angle. We find unique "ultra-soft" phason modes (frequency $\lesssim 1\ \mathrm{cm^{-1}}$, comparable to acoustic modes) for any non-zero twist, corresponding to an \textit{effective} translation of the moir{\'e} lattice by relative displacement of the constituent layers in a non-trivial way. Unlike the acoustic modes, the velocity of the phason modes is quite sensitive to twist angle. As twist angle decreases, ($\theta \lesssim 3^{\circ},\ \gtrsim 57^{\circ}$) the ultra-soft modes represent the acoustic modes of the "emergent" soft moir{\'e} scale lattice. Also, new high-frequency SMs appear, identical to those in stable bilayer TMD ($\theta = 0\degree/60\degree$), due to the overwhelming growth of stable stacking regions in relaxed twisted structures. Furthermore, we find remarkably different structural relaxation as $\theta \to 0^{\circ}$, $\to 60^{\circ}$ due to sub-lattice symmetry breaking. Our study reveals the possibility of an intriguing $\theta$ dependent superlubric to pinning behavior and of the existence of ultra-soft modes in \textit{all} two-dimensional (2D) materials.

Layer breathing and shear modes in multilayer graphene: a DFT-vdW study

In this work, we study structural and vibrational properties of multilayer graphene using density-functional theory with van der Waals (vdW) functionals. Initially, we analyze how different vdW functionals compare by evaluating the lattice parameters, elastic constants and vibrational frequencies of low energy optical modes of graphite. Our results indicate that the vdW-DF1-optB88 functional has the best overall performance on the description of vibrational properties. Next, we use this functional to study the influence of the vdW interactions on the structural and vibrational properties of multilayer graphene. Specifically, we evaluate binding energies, interlayer distances and phonon frequencies of layer breathing and shear modes. We observe excellent agreement between our calculated results and available experimental data, which suggests that this functional has truly predictive power for layer-breathing and shear frequencies that have not been measured yet. This indicates that careful selected vdW functionals can describe interlayer bonding in graphene-related systems with good accuracy.

Temperature-dependent layer breathing modes in two-dimensional materials

Relative out-of-plane displacements of the constituent layers of two-dimensional materials give rise to unique low-frequency breathing modes. By computing the height-height correlation functions from molecular dynamics simulations, we show that the layer breathing modes (LBMs) can be mapped consistently to vibrations of a simple linear chain model. Our calculated thickness dependence of LBM frequencies for few-layer (FL) graphene and molybdenum disulfide $({\mathrm{MoS}}_{2})$ are in excellent agreement with available experiments. Our results show a redshift of LBM frequency with an increase in temperature, which is a direct consequence of anharmonicities present in the interlayer interaction. We also predict the thickness and temperature dependence of LBM frequencies for FL hexagonal boron nitride. Our Rapid Communication provides a simple and efficient way to probe the interlayer interaction for layered materials and their heterostructures with the inclusion of anharmonic effects.

Graphite under compression: shift of layer breathing and shear modes frequencies with interlayer spacing

Layered materials have huge potential in various applications due to their extraordinary properties. To determine the interlayer interaction (or equivalently the layer spacing under different perturbations) is of critical importance. In this paper, we focus on one of the most prominent layered materials, graphite, and theoretically quantify the relationship between its interlayer spacing and the vibrational frequencies of its layer breathing and shear modes, which are measures of the interlayer interaction. The method used here to determine the interlayer interaction can be further applied to other layered materials.

Low-Frequency Shear and Layer-Breathing Modes in Raman Scattering of Two-Dimensional Materials

Ever since the isolation of single-layer graphene in 2004, two-dimensional layered structures have been among the most extensively studied classes of materials. To date, the pool of two-dimensional materials (2DMs) continues to grow at an accelerated pace and already covers an extensive range of fascinating and technologically relevant properties. An array of experimental techniques have been developed and used to characterize and understand these properties. In particular, Raman spectroscopy has proven to be a key experimental technique, thanks to its capability to identify minute structural and electronic effects in nondestructive measurements. While high-frequency (HF) intralayer Raman modes have been extensively employed for 2DMs, recent experimental and theoretical progress has demonstrated that low-frequency (LF) interlayer Raman modes are more effective at determining layer numbers and stacking configurations and provide a unique opportunity to study interlayer coupling. These advantages are due to 2DMs' unique interlayer vibration patterns where each layer behaves as an almost rigidly moving object with restoring forces corresponding to weak interlayer interactions. Compared to HF Raman modes, the relatively small attention originally devoted to LF Raman modes is largely due to their weaker signal and their proximity to the strong Rayleigh line background, which previously made their detection challenging. Recent progress in Raman spectroscopy with technical and hardware upgrades now makes it possible to probe LF modes with a standard single-stage Raman system and has proven crucial to characterize and understand properties of 2DMs. Here, we present a comprehensive and forward-looking review on the current status of exploiting LF Raman modes of 2DMs from both experimental and theoretical perspectives, revealing the fundamental physics and technological significance of LF Raman modes in advancing the field of 2DMs. We review a broad array of materials, with varying thickness and stacking configurations, discuss the effect of in-plane anisotropy, and present a generalized linear chain model and interlayer bond polarizability model to rationalize the experimental findings. We also discuss the instrumental improvements of Raman spectroscopy to enhance and separate LF Raman signals from the Rayleigh line. Finally, we highlight the opportunities and challenges ahead in this fast-developing field.

Probing the shear and layer breathing modes in multilayer graphene by Raman spectroscopy

The measurements of interlayer vibrations in multilayer graphene (MLG) have triggered a huge effort to understand phonons, electron–electron, electron–phonon, magneto–phonon interactions and the effect of layer number, stacking sequences, and layer orientations on the Raman spectroscopy of MLG. Here, we provide a review on the optical probe of interlayer vibrations, comprising the shear (C) and layer breathing (LB) modes. At first, we discuss different symmetries of MLGs in AB, ABC, and twisted stacking with an example of trilayer graphene, which dramatically influence the observations of interlayer vibrations. Then a brief description about the physical origins of the C and LB modes is introduced. Finally, two ways are elucidated to probe the interlayer modes in detail. The C and LB modes can be directly probed in the ultralow‐wavenumber Raman spectroscopy with special configurations, as depicted by the Raman spectra in MLG with diverse stacking orders. On the other hand, the LB modes can also be derived from the two‐phonon overtones in doubly resonant Raman spectra. These approaches can be extended to the other two‐dimensional layered materials, which pave the way to measure the interlayer coupling from experiments and thus greatly benefit the future research studies on their fundamental physics and potential applications. Copyright © 2017 JohnWiley &amp; Sons, Ltd.

Interfacial Interactions in van der Waals Heterostructures of MoS2 and Graphene.

Interfacial coupling between neighboring layers of van der Waals heterostructures (vdWHs), formed by vertically stacking more than two types of two-dimensional materials (2DMs), greatly affects their physical properties and device performance. Although high-resolution cross-sectional scanning tunneling electron microscopy can directly image the atomically sharp interfaces in the vdWHs, the interfacial coupling and lattice dynamics of vdWHs formed by two different types of 2DMs, such as semimetal and semiconductor, are not clear so far. Here, we report the ultralow-frequency Raman spectroscopy investigation on interfacial couplings in the vdWHs formed by graphene and MoS2 flakes. Because of the significant interfacial layer-breathing couplings between MoS2 and graphene flakes, a series of layer-breathing modes with frequencies dependent on their layer numbers are observed in the vdWHs, which can be described by the linear chain model. It is found that the interfacial layer-breathing force constant between MoS2 and graphene, α0⊥(I) = 60 × 1018 N/m3, is comparable with the layer-breathing force constant of multilayer MoS2 and graphene. The results suggest that the interfacial layer-breathing couplings in the vdWHs formed by MoS2 and graphene flakes are not sensitive to their stacking order and twist angle between the two constituents. Our results demonstrate that the interfacial interlayer coupling in vdWHs formed by two-dimensional semimetals and semiconductors can lead to new lattice vibration modes, which not only can be used to measure the interfacial interactions in vdWHs but also is beneficial to fundamentally understand the properties of vdWHs for further engineering the vdWHs-based electronic and photonic devices.

Excitation energy dependence of Raman spectra of few-layer WS2

Raman spectra of few-layer WS2 have been measured with up to seven excitation energies, and peculiar resonance effects are observed. The two-phonon acoustic phonon scattering signal close to the main E2g1 peak is stronger than the main peaks for excitations near the A or B exciton states. The low-frequency Raman spectra show a series of shear and layer-breathing modes that are useful for determining the number of layers. In addition, hitherto unidentified peaks (X1 and X2), which do not seem to depend on the layer thickness, are observed near resonances with exciton states. The polarization dependences of the two peaks are different: X1 vanishes in cross polarization, but X2 does not. At the resonance with the A exciton state, the Raman-forbidden, lowest-frequency shear mode for odd number of layers appears as strong as that for the allowed case of even number of layers. This mode also exhibits a strong Breit-Wigner-Fano line shape and an anomalous polarization behavior at this resonance.