In 2004, Geim and Novoselov successfully exfoliated monolayer graphene, a true two-dimensional (2D) materials[
Journal of Semiconductors, Volume. 40, Issue 9, 091001(2019)
Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure
Research on two-dimensional (2D) materials and related van der Waals heterostructures (vdWHs) is intense and remains one of the leading topics in condensed matter physics. Lattice vibrations or phonons of a vdWH provide rich information, such as lattice structure, phonon dispersion, electronic band structure and electron–phonon coupling. Here, we provide a mini review on the lattice vibrations in vdWHs probed by Raman spectroscopy. First, we introduced different kinds of vdWHs, including their structures, properties and potential applications. Second, we discussed interlayer and intralayer phonon in twist multilayer graphene and MoS2. The frequencies of interlayer and intralayer modes can be reproduced by linear chain model (LCM) and phonon folding induced by periodical moiré potentials, respectively. Then, we extended LCM to vdWHs formed by distinct 2D materials, such as MoS2/graphene and hBN/WS2 heterostructures. We further demonstrated how to calculate Raman intensity of interlayer modes in vdWHs by interlayer polarizability model.
1. Introduction
In 2004, Geim and Novoselov successfully exfoliated monolayer graphene, a true two-dimensional (2D) materials[
Figure 1.(Color online) Structure of several 2DMs (graphene, TMDs and hBN) and related vdWHs, such as twisted bilayer MoS
The intrinsic or modulated properties of 2DMs and vdWHs has been characterized by a large variety of spectroscopic methods[
The interlayer modes in 2DMs and vdWHs, corresponding to layer-layer vibrations, are sensitive to interlayer coupling, which can be well described by linear chain mode (LCM)[
where the
And the
For bulk counterpart of 2DM flakes,
Several branches of the S and LB modes have been observed in 2H-MoS2 flakes[
Here, we briefly give an up-to-date overview on the lattice vibrations in vdWHs studied by Raman spectroscopy. First, we discuss interlayer coupling in twisted multilayer graphene (tMLG). Then, twist-angle (
2. Lattice vibrations in twisted multilayer 2DMs
We first discuss vdWHs formed by 2DM flakes with the same monolayer counterpart, i.e., the so-called twisted multilayer 2DMs. We show that the twist in twisted multilayer 2DMs modify the lattice symmetry from their constitutes and make more interlayer vibration modes be observed. The different interfacial coupling between the S and LB modes in twisted multilayer 2DMs make the atomic displacement of the S modes be localized in the constitutes and that of the LB modes be extended over the whole twisted multilayer 2DMs. The moiré patterns can be formed in twisted multilayer 2DMs to create moiré superlattices stemming from periodic interlayer interaction potentials. The moiré superlattices can result in the zone folding effect for the phonon dispersion curve of each constituent, which can be used to probe the phonon dispersion curves of monolayer constituents.
2.1. Interlayer lattice vibrations in twisted multilayer graphene
In AB-stacked NLG (AB-NLG), only the branch of the shear modes with the highest frequency has been observed[
As presented in Fig. 2(a), optical contrast of t
Figure 2.(Color online) (a) Optical contrast of a flake comprising a t(1+1)LG and a t(1+3)LG[
To reproduce the interlayer modes in t
2.2. Moiré phonons in twisted bilayer MoS
The lattice structure of twisted bilayer 2DMs can be rigorously periodic to form the crystallographic superlattice, where the superlattice vectors of the two monolayer constituents match with each other, giving a finite unit cell. The lattice structure of the crystallographic superlattice can be represented by a pair of mutual prime numbers (
Figure 3.(Color online) (a) The reciprocal lattice of t2LM with
Raman spectra in the low frequency region of t2LM, 2H- and 3R-stacked MoS
Due to the periodic potential in crystallographic and moiré superlattices, the off-center phonons in the monolayer constituent linked with the corresponding reciprocal lattice vectors can be folded back to the
Because the phonon folding effect related to moiré phonons is mastered by the basic vector of moiré reciprocal lattices, rather than by that in the reciprocal lattices of crystallographic superlattices of t2LM, this study can be extended to other twisted bilayer 2DMs and the related vdWHs.
3. Lattice vibrations in vdWHs formed by different 2DMs
The interfacial coupling in vdWHs between different 2DM constitutes with distinct properties is also important for their fundamental research and application. Here, we discuss two vdWHs formed by different 2DMs, such as semimetal graphene and semiconductor MoS2, and insulator hBN and semiconductor WS2. It shows that interfacial coupling in vdWHs plays significant role in their vibration properties.
3.1. Interlayer coupling in MoS
Fig. 4(a) presents Raman spectra of vdWHs formed from bilayer MoS2 (2LM) and nLG, denoted as 2LM/nLG, where three branches of the LB modes (LB
Figure 4.(Color online) (a) Raman spectra of 2LM/
The S modes of 2LM/nLG vdWHs show almost identical peak position to that of 2LM, which indicates that the observed S mode in 2LM/nLG vdWHs is mainly localized in the 2LM constituent. The weaken interfacial shear coupling had also been observed in other mLM/nLG vdWHs and tMLG. The mismatched lattices between graphene and MoS
Interfacial layer-breathing coupling in vdWHs formed by semimetals and semiconductors induces new LB modes, which not only can be used to measure the interfacial interactions in vdWHs but also is beneficial to identify the total thickness of vdWHs. However, the S modes are localized in the constituents and thus they can be used to determine the numner of layers of the constituents in vdWHs.
The intralayer Raman modes in graphene/MoS
3.2. Cross-dimensional electron-phonon coupling in hBN/WS
The LCM demonstrated by the examples of
Figure 5.(Color online) (Color online) (a) Schematic diagram for constituent-vdWHs EPC of the LB modes in hBN/WS2 vdWHs, and Raman spectra of a 39L-hBN/3LW in the region of 5–50 cm–1. The triangles represent the expected LB modes in the 39L-hBN/3LW based on the LCM. (b) The modulus square of the projection from wavefunction of different LB modes in 39L-hBN/3LW vdWH onto the wavefunction of the LB
To understand this cross-dimensional electron–phonon coupling (EPC), a microscopic picture mediated by the interfacial coupling is proposed to calculate the relative Raman intensity of the LB modes in vdWHs[
The models presented above can be generalized and extended to other vdWHs. The cross-dimensional electron-phonon coupling in vdWHs provides a way to manipulate both the designable phonon excitations in vdWHs and their coupling to the electronic states by varying the constituents and engineering the interface.
4. Conclusion
This review presents application of Raman spectroscopy to investigate the lattice vibrations in twisted bilayer and multilayer 2DMs and vdWHs formed by different constituents. We introduce LCM to understand the interlayer vibration modes in 2DMs, which can also be extended to vdWHs and reproduce their interlayer Raman modes. From the experimental shear and LB modes, the interlayer shear and LB coupling strength in individual components and interface can be obtained, respectively. Furthermore, the interlayer coupling in twisted bilayer 2DMs induces periodic moiré potential, which modifies the lattice vibrations of monolayer constituent to form moiré phonons. By varying the twist angle, the moiré phonons of twisted bilayer 2DMs can be exploited to map the phonon dispersions of the monolayer constituent. Because of the significant interfacial layer-breathing couplings between the two constituents, many new LB modes with frequencies dependent on their layer numbers are observed in MoS2/graphene and WS2/hBN vdWHs. Because of the large lattice mismatch between two constituents, the interfacial LB couplings are not sensitive to their stacking order and twist angle in vdWHs. The flexible van der Waals stacking in vdWHs leads to multiple opportunities to engineer the interlayer phonon modes for cross-dimensional electron-phonon coupling.
Acknowledgments
We acknowledge support from the National Key Research and Development Program of China (Grant No. 2016YFA0301204), the National Natural Science Foundation of China (Grant Nos.11874350 and 11434010).
[1] K S Novoselov, m A K Geim, v S V Morozov et al. Electric field effect in atomically thin carbon films. Science, 306, 666(2004).
[2] G Fiori, F Bonaccorso, G Iannaccone et al. Electronics based on two-dimensional materials. Nat Nanotechnol, 9, 768(2014).
[3] N Mounet, M Gibertini, P Schwaller et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat Nanotechnol, 13, 246(2018).
[4] K S Novoselov, m A K Geim, S V Morozov et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 438, 197(2005).
[5] K F Mak, C G Lee, J Hone et al. Atomically thin MoS2: A new direct-gap semiconductor. Phys Rev Lett, 105, 136805(2010).
[6] X L Li, n W P Han, u J B Wu et al. Layer-number dependent optical properties of 2D materials and their application for thickness determination. Adv Funct Mater, 27, 1604468(2017).
[7] J B Wu, X Z Zhang, M Ijäs et al. Resonant Raman spectroscopy of twisted multilayer graphene. Nat Commun, 5, 5309(2014).
[8] J B Wu, u Z X Hu, X Zhang et al. Interface coupling in twisted multilayer graphene by resonant Raman spectroscopy of layer breathing modes. ACS Nano, 9, 7440(2015).
[9] J B Wu, n M L Lin, X Cong et al. Raman spectroscopy of graphene-based materials and its applications in related devices. Chem Soc Rev, 47, 1822(2018).
[10] Y Liu, Y Huang, n X F Duan. Van der Waals integration before and beyond twodimensional materials. Nature, 567, 323(2019).
[11] K S Novoselov, o A Mishchenko, o A Carvalho et al. 2D materials and van der Waals heterostructures. Science, 353, aac9439(2016).
[12] A K Geim, I V Grigorieva. Van der Waals heterostructures. Nature, 499, 419(2013).
[13] M L Lin, Q H Tan, u J B Wu et al. Moiré phonons in twisted bilayer MoS2. ACS Nano, 12, 8770(2018).
[14] H Y Yu, u G B Liu, J J Tang. Moiré excitons: From programmable quantum emitter arrays to spin-orbit-coupled artificial lattices. Sci Adv, 3, e1701696(2017).
[15] K L Seyler, P Rivera, H Y Yu et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature, 567, 66(2019).
[16] K Tran, G Moody, F C Wu et al. Evidence for moiré excitons in van der Waals heterostructures. Nature, 567, 71(2019).
[17] C H Jin, n E C Regan, A M Yan et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature, 567, 76(2019).
[18] Z Q Zhou, Y Cui, P H Tan et al. Optical and electrical properties of two-dimensional anisotropic materials. J Semicond, 40, 061001(2019).
[19] X Zhang, o X F Qiao, W Shi et al. Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. Chem Soc Rev, 44, 2757(2015).
[20]
[21] L B Liang, J Zhang, r B G Sumpter et al. Low-frequency shear and layer-breathing modes in raman scattering of twodimensional materials. ACS Nano, 11, 11777(2017).
[22] P H Tan, W P Han, W J Zhao et al. The shear mode of multilayer graphene. Nat Mater, 11, 294(2012).
[23] X Zhang, W P Han, J B Wu et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS2. Phys Rev B, 87, 115413(2013).
[24] M L Lin, Y Zhou, u J B Wu et al. Cross-dimensional electron-phonon coupling in van der Waals heterostructures. Nat Commun, 10, 2419(2019).
[25] Q J Song, Q H Tan, g X Zhang et al. Physical origin of davydov splitting and resonant Raman spectroscopy of davydov components in multilayer MoTe2. Phys Rev B, 93, 115409(2016).
[26] Q H Tan, X Zhang, o X D Luo et al. Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings. J Semicond, 38, 031006(2017).
[27] J B Wu, H Wang, X L Li et al. Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition. Carbon, 110, 225(2016).
[28] M L Lin, T Chen, W Lu et al. Identifying the stacking order of multilayer graphene grown by chemical vapor deposition via Raman spectroscopy. J Raman Spectrosc, 49, 46(2018).
[29] H Li, u J B Wu, F R Ran et al. Interfacial interactions in van der Waals heterostructures of MoS2 and graphene. ACS Nano, 11, 11714(2017).
[30] J H Yang, e J U Lee, g H Cheong. Excitation energy dependence of Raman spectra of few-layer WS2. FlatChem, 3, 64(2017).
[31] L B Liang, y A A Puretzky, r B G Sumpter et al. Interlayer bond polarizability model for stacking-dependent low-frequency Raman scattering in layered materials. Nanoscale, 9, 15340(2017).
Get Citation
Copy Citation Text
Xin Cong, Miaoling Lin, Ping-Heng Tan. Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure[J]. Journal of Semiconductors, 2019, 40(9): 091001
Category: Reviews
Received: Aug. 6, 2019
Accepted: --
Published Online: Sep. 22, 2021
The Author Email: