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## About this book

This book shows the electronic, optical and lattice-vibration properties of the two-dimensional materials which are revealed by the Raman spectroscopy. It consists of eleven chapters covering various Raman spectroscopy techniques (ultralow-frequency, resonant Raman spectroscopy, Raman imaging), different kinds of two-dimensional materials (in-plane isotropy and anisotropy materials, van der Waals heterostructures) and their physical properties (double-resonant theory, surface and interface effect). The topics include the theory origin, experimental phenomenon and advanced techniques in this area. This book is interesting and useful to a wide readership in various fields of condensed matter physics, materials science and engineering.

## Table of Contents

### Chapter 1. Raman Spectroscopy of Monolayer and Multilayer Graphenes

Abstract
The discovery of monolayer graphene in 2004 has triggered a great effort to investigate the fundamental properties and applications of all two-dimensional materials (2DMs). Monolayer graphene (1LG) can be stacked layer by layer in a particular way (AB, ABC and twist) to form multilayer graphene (MLG), whose properties vary according to the stacking. Raman spectroscopy is a useful tool to reveal the chemical and physical properties of graphene materials. In this chapter, we review the systematic development of the Raman spectroscopy of pristine 1LG and MLG. The essential Raman scattering processes of the entire first and second order modes in intrinsic 1LG are addressed in detail. We further introduce the concept of double resonance Raman scattering in graphene. Moreover, a series of works on the shear (C), layer-breathing (LB) and 2D modes of MLGs with different stacking orders are discussed. Finally, various types of resonance Raman spectroscopy of 1LG and MLG are also presented. The Raman spectroscopy of graphene materials can serve as a typical example in studying the Raman spectroscopy of other 2DMs and introducing the fundamental physical concepts for 2DMs.
Jiang-Bin Wu, Miao-Ling Lin, Ping-Heng Tan

### Chapter 2. Raman Spectroscopy of Isotropic Two-Dimensional Materials Beyond Graphene

Abstract
In this chapter, we will focus on the isotropic (or rather less anisotropic) two-dimensional layered materials, including the layered transition metal dichalcogenides, the topologically insulating Bi2X3 (X = Se, Te) etc.
Xin Lu, Qing-Hai Tan, Qihua Xiong, Jun Zhang

### Chapter 3. Raman Spectroscopy of Anisotropic Two-Dimensional Materials

Abstract
Due to the in-plane structural anisotropy, two-dimensional (2D) layered materials with low symmetry exhibit unique crystalline-axis dependent properties, including the optical, mechanical and electrical properties. Raman spectroscopy, in particular, polarized Raman spectroscopy, has been used as a rapid and non-invasive technique to study the composition, structure and symmetry of 2D anisotropic layered materials. In this chapter, the recent advances on the Raman spectroscopic studies of anisotropic 2D materials are summarized. The Raman selection rules and the structural symmetry will be discussed, followed by the overview of the polarized Raman scattering studies of anisotropic 2D materials cataloged by crystal symmetries.
Juanxia Wu, Shishu Zhang, Lianming Tong, Jin Zhang

### Chapter 4. Raman Spectroscopy of van der Waals Heterostructures

Abstract
The research of two-dimensional (2D) atomic crystals has progressed rapidly since the isolation of graphene in 2004 [1, 2]. The family of 2D crystals now include many different types of materials, including metals (e.g. graphene, NbSe2), semiconductors (e.g. phosphorene, MoS2, WSe2), insulators (e.g. BN), superconductors and charge-density-wave materials (e.g. NbSe2 and TiSe2). Alongside with the rapid development of individual 2D materials, the research frontier has also advanced to explore their hybrid systems [3, 4]. In particular, the flat and inert surfaces of 2D materials enable the construction of heterogeneous stacks of different 2D crystals with atomically sharp interfaces, coupled vertically only by van der Waals forces. These van der Waals heterostructures exhibit many unique properties that cannot be realized in individual 2D crystals [3, 4]. For instance, graphene on hexagonal boron nitride (BN) can exhibit the Hofstadter’s butterfly phenomenon because of the nanoscale periodic interaction between the graphene and BN lattices [5–7]. Transition metal dichalcogenide (TMD) heterostructures can host long-lived interlayer excitons due to the staggered band alignment between different TMD layers [8]. Electronic and optoelectronic devices made from van der Waals heterostructures can exhibit performance superior to that of traditional devices with lateral 2D junctions [9–11]. More generally, the 2D building blocks can be combined to form more complex structures. By incorporating the unique properties of each class of 2D crystal (e.g., semiconducting TMDs, insulating BN and metallic graphene), integrated circuits can in principle be constructed entirely with 2D materials. Such 2D systems of electronics, once realized, could open a route to post-silicon technology.
C. H. Lui

### Chapter 5. Disorder and Defects in Two-Dimensional Materials Probed by Raman Spectroscopy

Abstract
This paper describes the fundamentals of using Raman spectroscopy to characterize disorder in two-dimensional (2D) systems caused by the presence of defects. From the dimensionality point of view, in 2D crystalline structures disorder can be described as addition of point-like (zero-dimensional, 0D) or line-like (one-dimensional, 1D) defects. To characterize the amount of 0D and 1D defects separately, two spectral parameters are needed. The two basic parameters are related to defect-induced activation of forbidden Raman modes and to defect-induced confinement of phonons. A two-dimensional Raman phase diagram can be built based on geometrical considerations, and the geometrical parameters are governed by fundamental aspects such as phonon and electron coherence lengths and Raman cross sections. We apply the general picture to the well-studied case of graphene amorphization, which has been studied since the 70’ies, with the two basic parameters being represented by the peak linewidths (Γ) and by the integrated intensity ratio (AD/AG) between the defect-induced (D) mode and the Raman allowed graphene (G) mode. The amorphization of graphene has been fully described in the terms presented here thanks to the development of standard materials with well-controlled amount of either point-like or line-like defects.
Ado Jorio, Luiz Gustavo Cançado

### Chapter 6. Raman Spectroscopy Study of Two-Dimensional Materials Under Strain

Abstract
The exceptionally high stretchability of atomically thin materials enables extensive manipulation of their properties and exploration of rich physics through the application of external strain. Therefore, it is important to understand strain effects on two-dimensional materials both for fundamental studies and developing various applications, especially in flexible and wearable devices. In this chapter, we will give several examples of how Raman spectroscopy can be utilized to investigate the strain effects on fundamental properties of atomically thin materials.
Chunxiao Cong, Yanlong Wang, Ting Yu

### Chapter 7. Double Resonance Raman Spectroscopy of Two-Dimensional Materials

Abstract
In this chapter, we overview double resonance Raman spectra of two dimensional materials. Many weak Raman spectral peaks are observed in the two dimensional materials which can be attributed to second order, double resonance Raman spectra. It is useful for material characterization to understand not only first order Raman spectra but also second order Raman spectra since the second order Raman spectra has more information on electronic structure of the materials than the first order Raman spectra. Combined with the conventional first order resonance Raman theory, we will explain why the double resonance condition can be strong in the two dimensional materials. Since the double resonance Raman spectra give the information of phonon with non-zero wavevectors in the Brillouin zone, both the resonant wavevector and corresponding Raman spectra can shift with changing the incident laser energy. Here we will discuss the physics of double resonance Raman spectra of graphene, transition metal dichalcogenides by theoretical analysis using the first principles calculation.
R. Saito, Y. Tatsumi, T. Yang, H. Guo, S. Huang, L. Zhou, M. S. Dresselhaus

### Chapter 8. Raman Signatures of Surface and Interface Effects in Two-Dimensional Layered Materials: Theoretical Insights

Abstract
Raman spectroscopy is a non-destructive and versatile method of identifying materials through their Raman “fingerprints”. To this end, first principles calculations are essential to predict the Raman spectra of different materials. First principles calculations, together with parametrized models, can also give atomic scale insights into the origins of Raman shifts and Raman intensities, thus providing a guide to experiments. In this chapter, we will discuss some insights we have gained through our theoretical modeling of Raman spectra in 2D materials and their heterostructures. In particular, we show that surface and interface effects in 2D materials can give rise to observable changes in the Raman spectra. For example, we show that the formation of a surface in the 2D material leads to larger interatomic force constants at the surface, which results in experimentally observed anomalous frequency trends of the $${E}_{2g}^1$$ mode in MoS2, and the $${E}_{2g}^1$$ and $${B}_{2g}^1$$ modes in WSe2. We further show that the Raman intensities of the interlayer shear modes in 2D layered materials can be simply predicted based on the stacking sequence.
Sandhya Chintalapati, Xin Luo, Su Ying Quek

### Chapter 9. Resonant Raman Spectroscopy of Two Dimensional Materials Beyond Graphene

Abstract
The resonance Raman effects in two dimensional materials including transition metal dichalcogenides and black phosphorus are reviewed. The Raman intensities of high-frequency intra-layer vibration modes are enhanced near resonance with exciton states. Some Raman peaks that are either forbidden or weak in non-resonant cases show strong enhancement near resonances. In the low-frequency Raman spectra, some unusual features, in addition to shear and breathing modes, appear near resonance with exciton states. Some intra-layer vibration modes exhibit Davydov splitting due to inter-layer interactions when the excitation energy is close to resonances. The polarization behaviors of some Raman modes in anisotropic two-dimensional materials have peculiar dependences on the excitation energy, which is related to the resonance effect.
Hyeonsik Cheong, Jae-Ung Lee

### Chapter 10. Ultralow-Frequency Raman Spectroscopy of Two-dimensional Materials

Abstract
In two-dimensional materials (2DMs), atoms within one layer (in-plane) are joined by covalent bonds, whereas van der Waals (vdW) interactions keep the layers together. Raman spectroscopy is a powerful tool for measuring the lattice vibrational modes in 2DMs, including the intralayer and interlayer vibrations, and has shown great potential for the characterizations of the layer number, interlayer coupling and layer-stacking configurations in 2DMs via the ultralow-frequency (ULF) interlayer vibrational modes. This chapter begins with an introduction of how the monolayer 2DMs stack to assemble a large family of two-dimensional systems (Section 10.1), which are likely to exhibit modified interlayer coupling and thus various ULF mode behaviours. In sequence, Section 10.2 provides a detailed description of the physical origins of the interlayer vibrations and the linear chain model (LCM) to depict their layer-number dependent frequencies. Subsequently, two popular Raman setups are introduced to perform the ULF modes measurements (Section 10.3). Then, we provide a review of the ULF Raman spectroscopy of various types of 2DMs, including: (1) layer-number dependent (Section 10.4.1) and (2) stacking-order dependent (Section 10.4.2) ULF Raman spectroscopy in isotropic 2DMs; (3) ULF Raman spectroscopy in anisotropic 2DMs(Section 10.4.3); and (4) ULF Raman modes in twisted 2DMs (Section 10.4.4) and heterostructures (Section 10.4.5).
Miao-Ling Lin, Ping-Heng Tan

### Chapter 11. Raman Imaging of Two Dimensional Materials

Abstract
Raman imaging is a powerful technique that can provide the spatial distribution of the properties of the micro-/nano- material. Different parameters of the Raman peaks, e.g. height/area, position, full width at half maximum (FWHM), and also ratios/differences between peaks, can be used to construct the Raman imaging and provide valuable information for the study of 2D materials and heterostructure. In this chapter, we will introduce the basic principle of Raman imaging, and also its application in the study of 2D materials, including the effects of thickness and stacking configurations, heterostructure and interlayer coupling, defects, strain. We will also show that Raman imaging is an ideal tool to study the growth mechanism of CVD graphene.
Xuhong An, Zhenhua Ni, Zexiang Shen

### Correction to: Raman Spectroscopy of Two-Dimensional Materials

Ping-Heng Tan
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