Layer Breathing Modes Research Articles

Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings**Project supported by the National Basic Research Program of China (No. 2016YFA0301200), the National Natural Science Foundation of China (Nos. 11225421, 11474277, 11434010, 61474067, 11604326, 11574305 and 51527901), and the National Young 1000 Talent Plan of China.

Two-dimensional transition metal dichalcogenides (TMDs) have attracted extensive attention due to their many novel properties. The atoms within each layer in two-dimensional TMDs are joined together by covalent bonds, while van der Waals interactions combine the layers together. This makes its lattice dynamics layer-number dependent. The evolutions of ultralow frequency (< 50 cm−1) modes, such as shear and layer-breathing modes have been well-established. Here, we review the layer-number dependent high-frequency (> 50 cm−1) vibration modes in few-layer TMDs and demonstrate how the interlayer coupling leads to the splitting of high-frequency vibration modes, known as Davydov splitting. Such Davydov splitting can be well described by a van der Waals model, which directly links the splitting with the interlayer coupling. Our review expands the understanding on the effect of interlayer coupling on the high-frequency vibration modes in TMDs and other two-dimensional materials.

Physical origin of Davydov splitting and resonant Raman spectroscopy of Davydov components in multilayerMoTe2

We systematically study the high-resolution and polarized Raman spectra of multilayer (ML) MoTe2. The layer-breathing (LB) and shear (C) modes are observed in the ultralow-frequency region, which are used to quantitatively evaluate the interlayer coupling in ML MoTe2 based on the linear chain model, in which only the nearest interlayer coupling is considered. The Raman spectra on three different substrates verify the negligible substrate effect on the phonon frequencies of ML MoTe2. Ten excitation energies are used to measure the high-frequency modes of N-layer MoTe2 (NL MoTe2; N is an integer). Under the resonant excitation condition, we observe N-dependent Davydov components in ML MoTe2 , originating from the Raman-active A'1(A21g) modes at ~172 cm-1. More than two Davydov components are observed in NL MoTe2 for N larger than 4 by Raman spectroscopy. The N-dependent Davydov components are further investigated based on the symmetry analysis. A van der Waals model only considering the nearest interlayer coupling has been proposed to well understand the Davydov splitting of high-frequency A'1(A21g) modes. The different resonant profiles for the two Davydov components in 3L MoTe2 indicate that proper excitation energy of ~1.8-2.2 eV must be chosen to observe the Davydov splitting in ML MoTe2 . Our work presents a simple way to identify layer number of ultrathin MoTe2 flakes by the corresponding number and peak position of Davydov components. Our work also provides a direct evidence from Raman spectroscopy of how the nearest van der Waals interactions significantly affect the frequency of the high-frequency intralayer phonon modes in multilayer MoTe2 and expands the understanding on the lattice vibrations and interlayer coupling of transition metal dichalcogenides and other two-dimensional materials.

Determining layer number of two-dimensional flakes of transition-metal dichalcogenides by the Raman intensity from substrates

Transition-metal dichalcogenide (TMD) semiconductors have been widely studied due to their distinctive electronic and optical properties. The property of TMD flakes is a function of their thickness, or layer number (N). How to determine the N of ultrathin TMD materials is of primary importance for fundamental study and practical applications. Raman mode intensity from substrates has been used to identify the N of intrinsic and defective multilayer graphenes up to N = 100. However, such analysis is not applicable to ultrathin TMD flakes due to the lack of a unified complex refractive index () from monolayer to bulk TMDs. Here, we discuss the N identification of TMD flakes on the SiO2/Si substrate by the intensity ratio between the Si peak from 100 nm (or 89 nm) SiO2/Si substrates underneath TMD flakes and that from bare SiO2/Si substrates. We assume the real part of of TMD flakes as that of monolayer TMD and treat the imaginary part of as a fitting parameter to fit the experimental intensity ratio. An empirical namely, of ultrathin MoS2, WS2 and WSe2 flakes from monolayer to multilayer is obtained for typical laser excitations (2.54 eV, 2.34 eV or 2.09 eV). The fitted of MoS2 has been used to identify the N of MoS2 flakes deposited on 302 nm SiO2/Si substrate, which agrees well with that determined from their shear and layer-breathing modes. This technique of measuring Raman intensity from the substrate can be extended to identify the N of ultrathin 2D flakes with N-dependent For application purposes, the intensity ratio excited by specific laser excitations has been provided for MoS2, WS2 and WSe2 flakes and multilayer graphene flakes deposited on Si substrates covered by a 80–110 nm or 280–310 nm SiO2 layer.

Mapping of Low-Frequency Raman Modes in CVD-Grown Transition Metal Dichalcogenides: Layer Number, Stacking Orientation and Resonant Effects.

Layered inorganic materials, such as the transition metal dichalcogenides (TMDs), have attracted much attention due to their exceptional electronic and optical properties. Reliable synthesis and characterization of these materials must be developed if these properties are to be exploited. Herein, we present low-frequency Raman analysis of MoS2, MoSe2, WSe2 and WS2 grown by chemical vapour deposition (CVD). Raman spectra are acquired over large areas allowing changes in the position and intensity of the shear and layer-breathing modes to be visualized in maps. This allows detailed characterization of mono- and few-layered TMDs which is complementary to well-established (high-frequency) Raman and photoluminescence spectroscopy. This study presents a major stepping stone in fundamental understanding of layered materials as mapping the low-frequency modes allows the quality, symmetry, stacking configuration and layer number of 2D materials to be probed over large areas. In addition, we report on anomalous resonance effects in the low-frequency region of the WS2 Raman spectrum.

Observation of anisotropic interlayer Raman modes in few‐layer ReS2

ReS2 has recently emerged as a new member in the rapidly growing family of two‐dimensional materials. Unlike MoS2 or WSe2, the optical and electrical properties of ReS2 are not isotropic due to the reduced symmetry of the crystal. Here, we present layer‐dependent Raman measurements of ReS2 samples ranging from monolayers to ten layers in the ultralow frequency regime. We observe layer breathing and shear modes which allow for easy assignment of the number of layers. Polarization‐dependent measurements give further insight into the crystal structure and reveal an energetic shift of the shear mode which stems from the in‐plane anisotropy of the shear modulus in this material. (© 2016 WILEY‐VCH Verlag GmbH &amp;Co. KGaA, Weinheim)

Low wavenumber Raman spectroscopy of highly crystalline MoSe2grown by chemical vapor deposition

Transition metal dichalcogenides (TMDs) have recently attracted attention due to their interesting electronic and optical properties. Fabrication of these materials in a reliable and facile method is important for future applications, as are methods to characterize material quality. Here we present the chemical vapor deposition of MoSe2 monolayer and few layer crystals. These results show the practicality of using chemical vapor deposition to reliably fabricate these materials. Low frequency Raman spectra and mapping of shear and layer breathing modes of MoSe2 are presented for the first time. We correlate the behavior of these modes with layer number in the materials. The usefulness of low frequency Raman mapping to probe the symmetry, quality, and monolayer presence in CVD grown 2D materials is emphasized. Raman map of maximum intensity position for low wavenumber shear and layer breathing modes of MoSe2.

Interface Coupling in Twisted Multilayer Graphene by Resonant Raman Spectroscopy of Layer Breathing Modes.

Raman spectroscopy is the prime nondestructive characterization tool for graphene and related layered materials. The shear (C) and layer breathing modes (LBMs) are due to relative motions of the planes, either perpendicular or parallel to their normal. This allows one to directly probe the interlayer interactions in multilayer samples. Graphene and other two-dimensional (2d) crystals can be combined to form various hybrids and heterostructures, creating materials on demand with properties determined by the interlayer interaction. This is the case even for a single material, where multilayer stacks with different relative orientations have different optical and electronic properties. In twisted multilayer graphene there is a significant enhancement of the C modes due to resonance with new optically allowed electronic transitions, determined by the relative orientation of the layers. Here we show that this applies also to the LBMs, which can be now directly measured at room temperature. We find that twisting has a small effect on LBMs, quite different from the case of the C modes. This implies that the periodicity mismatch between two twisted layers mostly affects shear interactions. Our work shows that ultralow-frequency Raman spectroscopy is an ideal tool to uncover the interface coupling of 2d hybrids and heterostructures.

Substrate-free layer-number identification of two-dimensional materials: A case of Mo0.5W0.5S2 alloy

Any of two or more two-dimensional (2D) materials with similar properties can be alloyed into a new layered material, namely, 2D alloy. Individual monolayer in 2D alloys is kept together by van der Waals interactions. The property of multilayer alloys is a function of their layer number. Here, we studied the shear (C) and layer-breathing (LB) modes of Mo0.5W0.5S2 alloy flakes and their link to the layer number. The study reveals that the disorder effect is absent in the C and LB modes of 2D alloys, and the monatomic chain model can be used to estimate the frequencies of the C and LB modes. We demonstrated how to use the frequencies of C and LB modes to identify the layer number of alloy flakes deposited on different substrates. This technique is independent of the substrate, stoichiometry, monolayer thickness, and complex refractive index of 2D materials, offering a robust and substrate-free approach for layer-number identification of ultrathin flakes of 2D materials, such as 2D crystals and 2D alloys.

Stacking-dependent shear modes in trilayer graphene

We observe distinct interlayer shear mode Raman spectra for trilayer graphene with ABA and ABC stacking order. There are two rigid-plane shear-mode phonon branches in trilayer graphene. We find that ABA trilayers exhibit pronounced Raman response from the high-frequency shear branch, without any noticeable response from the low-frequency branch. In contrast, ABC trilayers exhibit no response from the high-frequency shear branch, but significant Raman response from the low-frequency branch. Such complementary behaviors of Raman shear modes can be explained by the distinct symmetry of the two trilayer allotropes. The strong stacking-order dependence is not found in the layer-breathing modes, and thus represents a unique characteristic of the shear modes.

Raman spectroscopy of shear and layer breathing modes in multilayer MoS2

We study by Raman scattering the shear and layer breathing modes in multilayer MoS2. These are identified by polarization measurements and symmetry analysis. Their positions change with the number of layers, with different scaling for odd and even layers. A chain model explains the results, with general applicability to any layered material, and allows one to monitor their thickness.

Measurement of layer breathing mode vibrations in few-layer graphene

Layer-layer coupling plays a critical role in defining the physical properties of few-layer graphene (FLG). With respect to vibrations, the interlayer coupling is predicted to create a set of N-1 finite frequency, out-of-plane interlayer modes in N-layer graphene. Unlike the widely studied in-plane vibrations, the properties of these layer-breathing modes (LBMs) are defined by the layer-layer interactions. Here we report direct observation of the distinct LBMs for graphene of thicknesses from 2 to 20 layers through electronically resonant overtone Raman bands observed in the range of 80 - 300 cm-1. The Raman bands exhibit multi-peak features that are unique for graphene samples of each layer thickness up to 20 layers. The frequencies of the set of layer breathing modes for all samples can be described within a simple model of nearest plane coupling.

Phonon Raman scattering in (La1-xSrx)2CuO4 single crystals.

Anomalous Raman spectra were observed in (${\mathrm{La}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${)}_{2}$${\mathrm{CuO}}_{4}$ single crystals for the light polarized parallel to the layer. The number of peaks are much larger than expected from group-theoretical analysis, supposely due to the strong phonon-magnon and phonon-free carrier interactions. With increasing x, two-phonon peaks decrease simultaneously with the decrease of the two-magnon peaks; this in turn is related with the decrease of the correlation length of the antiferromagnetic spin order. Two-phonon scattering is composed of a combination of two layer-breathing modes and two layer-quadratic modes, modes that have strong electron-phonon interaction. A soft mode for the orthorhombic-tetragonal phase transition was found for the incident light polarized perpendicular to the layer, its energy is much higher than that observed by neutron scattering. The present Raman scattering indicates that the symmetry of the crystal with x&gt;0.01 is lower than orthorhombic.