Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

Xin Cong; Miaoling Lin; Ping-Heng Tan

doi:10.1088/1674-4926/40/9/091001

J. Semicond. > 2019, Volume 40 > Issue 9 > 091001

REVIEWS

Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

Xin Cong^{1, 2}, Miaoling Lin^{1, 2} and Ping-Heng Tan^{1, 2, 3,}

+ Author Affiliations

Corresponding author: Ping-Heng Tan, E-mail: phtan@semi.ac.cn

DOI: 10.1088/1674-4926/40/9/091001

Abstract: 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.

Key words: two-dimensional materials, van der Waals heterostructure, Raman spectroscopy, lattice vibration, phonon

References

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696), 666 doi: 10.1126/science.1102896
[2]	Fiori G, Bonaccorso F, Iannaccone G, et al. Electronics based on two-dimensional materials. Nat Nanotechnol, 2014, 9(10), 768 doi: 10.1038/nnano.2014.207
[3]	Mounet N, Gibertini M, Schwaller P, et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat Nanotechnol, 2018, 13(3), 246 doi: 10.1038/s41565-017-0035-5
[4]	Novoselov K S, Geim A K, Morozov S V, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 2005, 438(7065), 197 doi: 10.1038/nature04233
[5]	Mak K F, Lee C G, Hone J, et al. Atomically thin MoS₂: A new direct-gap semiconductor. Phys Rev Lett, 2010, 105, 136805 doi: 10.1103/PhysRevLett.105.136805
[6]	Li X L, Han W P, Wu J B, et al. Layer-number dependent optical properties of 2D materials and their application for thickness determination. Adv Funct Mater, 2017, 27(19), 1604468 doi: 10.1002/adfm.201604468
[7]	Wu J B, Zhang X Z, Ijäs M, et al. Resonant Raman spectroscopy of twisted multilayer graphene. Nat Commun, 2014, 5, 5309 doi: 10.1038/ncomms6309
[8]	Wu J B, Hu Z X, Zhang X, et al. Interface coupling in twisted multilayer graphene by resonant Raman spectroscopy of layer breathing modes. ACS Nano, 2015, 9(7), 7440 doi: 10.1021/acsnano.5b02502
[9]	Wu J B, Lin M L, Cong X, et al. Raman spectroscopy of graphene-based materials and its applications in related devices. Chem Soc Rev, 2018, 47(5), 1822 doi: 10.1039/C6CS00915H
[10]	Liu Y, Huang Y, Duan X F. Van der Waals integration before and beyond twodimensional materials. Nature, 2019, 567(7748), 323 doi: 10.1038/s41586-019-1013-x
[11]	Novoselov K S, Mishchenko A, Carvalho A, et al. 2D materials and van der Waals heterostructures. Science, 2016, 353(6298), aac9439 doi: 10.1126/science.aac9439
[12]	Geim A K, Grigorieva I V. Van der Waals heterostructures. Nature, 2013, 499(7459), 419 doi: 10.1038/nature12385
[13]	Lin M L, Tan Q H, Wu J B, et al. Moiré phonons in twisted bilayer MoS₂. ACS Nano, 2018, 12(8), 8770 doi: 10.1021/acsnano.8b05006
[14]	Yu H Y, Liu G B, Tang J J. Moiré excitons: From programmable quantum emitter arrays to spin-orbit-coupled artificial lattices. Sci Adv, 2017, 3(11), e1701696 doi: 10.1126/sciadv.1701696
[15]	Seyler K L, Rivera P, Yu H Y, et al. Signatures of moiré-trapped valley excitons in MoSe₂/WSe₂ heterobilayers. Nature, 2019, 567(7746), 66 doi: 10.1038/s41586-019-0957-1
[16]	Tran K, Moody G, Wu F C, et al. Evidence for moiré excitons in van der Waals heterostructures. Nature, 2019, 567(7746), 71 doi: 10.1038/s41586-019-0975-z
[17]	Jin C H, Regan E C, Yan A M, et al. Observation of moiré excitons in WSe₂/WS₂ heterostructure superlattices. Nature, 2019, 567(7746), 76 doi: 10.1038/s41586-019-0976-y
[18]	Zhou Z Q, Cui Y, Tan P H, et al. Optical and electrical properties of two-dimensional anisotropic materials. J Semicond, 2019, 40, 061001 doi: 10.1088/1674-4926/40/6/061001
[19]	Zhang X, Qiao X F, Shi W, et al. Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. Chem Soc Rev, 2015, 44(9), 2757 doi: 10.1039/C4CS00282B
[20]	Tan P H. Raman Spectroscopy of two-dimensional materials. Singapore: Springer, 2019
[21]	Liang L B, Zhang J, Sumpter B G, et al. Low-frequency shear and layer-breathing modes in raman scattering of twodimensional materials. ACS Nano, 2017, 11(12), 11777 doi: 10.1021/acsnano.7b06551
[22]	Tan P H, Han W P, Zhao W J, et al. The shear mode of multilayer graphene. Nat Mater, 2012, 11(4), 294 doi: 10.1038/nmat3245
[23]	Zhang X, Han W P, Wu J B, et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS₂. Phys Rev B, 2013, 87(11), 115413 doi: 10.1103/PhysRevB.87.115413
[24]	Lin M L, Zhou Y, Wu J B, et al. Cross-dimensional electron-phonon coupling in van der Waals heterostructures. Nat Commun, 2019, 10(1), 2419 doi: 10.1038/s41467-019-10400-z
[25]	Song Q J, Tan Q H, Zhang X, et al. Physical origin of davydov splitting and resonant Raman spectroscopy of davydov components in multilayer MoTe₂. Phys Rev B, 2016, 93(11), 115409 doi: 10.1103/PhysRevB.93.115409
[26]	Tan Q H, Zhang X, Luo X D, et al. Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings. J Semicond, 2017, 38(3), 031006 doi: 10.1088/1674-4926/38/3/031006
[27]	Wu J B, Wang H, Li X L, et al. Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition. Carbon, 2016, 110, 225 doi: 10.1016/j.carbon.2016.09.006
[28]	Lin M L, Chen T, Lu W, et al. Identifying the stacking order of multilayer graphene grown by chemical vapor deposition via Raman spectroscopy. J Raman Spectrosc, 2018, 49(1), 46 doi: 10.1002/jrs.5219
[29]	Li H, Wu J B, Ran F R, et al. Interfacial interactions in van der Waals heterostructures of MoS₂ and graphene. ACS Nano, 2017, 11(11), 11714 doi: 10.1021/acsnano.7b07015
[30]	Yang J H, Lee J U, Cheong H. Excitation energy dependence of Raman spectra of few-layer WS₂. FlatChem, 2017, 3, 64 doi: 10.1016/j.flatc.2017.06.001
[31]	Liang L B, Puretzky A A, Sumpter B G, et al. Interlayer bond polarizability model for stacking-dependent low-frequency Raman scattering in layered materials. Nanoscale, 2017, 9(40), 15340 doi: 10.1039/C7NR05839J

Fig. 1. (Color online) Structure of several 2DMs (graphene, TMDs and hBN) and related vdWHs, such as twisted bilayer MoS$ _2 $ and twisted bilayer graphene with twisted angle $ \theta $, MoS$ _2 $/Graphene and WS$ _2 $/hBN heterostructure.

DownLoad: Full-Size Img PowerPoint

Fig. 2. (Color online) (a) Optical contrast of a flake comprising a t(1+1)LG and a t(1+3)LG^[7]. (b) Raman spectra in the spectral range of the C, LB and G modes for t(1+3)LG. Polarized Raman spectra are also shown to identify the C and LB modes^[8]. (c) Experimental (Exp., open diamonds) and theoretical (Theo., crosses) $ \omega $(C$ _{N,N-i} $) in t(m + n)LGs. The insert shows a schematic diagram of a linear chain model for t(2+3)LG including a bulk-like interlayer force constant $ \alpha_0^{\text{‖}}(G) $, interfacial force constant $ \alpha_t^{\text{‖}}(G) $ and the force constant $ \alpha_{0t}^{\text{‖}}(G) $ for the layers adjacent to the interface^[7].

DownLoad: Full-Size Img PowerPoint

Fig. 3. (Color online) (a) The reciprocal lattice of t2LM with $ \theta $ = $10.99^{\circ} $ and schematic diagram of moiré basic vectors ($ g_i $, i = 1,2,3) with $ \theta\leqslant 30^{\circ} $. Red dashed and green solid lines correspond to the BZ of moiré and crystallographic superlattice of the t2LMs, respectively. (b) Raman spectra of 3R- and 2H-2LMs and t2LMs with different $ \theta $ in the low-frequency region excited by E$ _{\rm ex} $ = 2.54 eV. (c) Raman spectra of $ t $2LMs with different $ \theta $ and monolayer MoS$ _2 $. Different shapes and color symbols represent the Raman modes from corresponding phonon branches. (d, e) The comparison of calculated and experimental frequencies of moiré phonons dependent on $ \theta $ and $ |{ g}_{\rm M}| $^[13].

DownLoad: Full-Size Img PowerPoint

Fig. 4. (Color online) (a) Raman spectra of 2LM/nLG in the S and LB peak spectral ranges. (b) Schematic diagram of a linear chain model (LCM) for the LB modes in 2LM/3LG, in which the next nearest LB coupling in the 3LG constituent is considered. (c) Pos(LB$ _{N,N-1} $) dependent on $ n $ of the nLG constituent. The solid lines show the theoretical trend of Pos(LB$ _{N,N-1} $) on $ n $ based on the improved LCM^[29].

DownLoad: Full-Size Img PowerPoint

Fig. 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$ _{3,2} $ mode in a standalone 3LW flake. (c) The relative intensity of LB modes in 39L-hBN/3LW vdWH based on the interlayer bond polarizability mode^[24].

DownLoad: Full-Size Img PowerPoint

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696), 666 doi: 10.1126/science.1102896
[2]	Fiori G, Bonaccorso F, Iannaccone G, et al. Electronics based on two-dimensional materials. Nat Nanotechnol, 2014, 9(10), 768 doi: 10.1038/nnano.2014.207
[3]	Mounet N, Gibertini M, Schwaller P, et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat Nanotechnol, 2018, 13(3), 246 doi: 10.1038/s41565-017-0035-5
[4]	Novoselov K S, Geim A K, Morozov S V, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 2005, 438(7065), 197 doi: 10.1038/nature04233
[5]	Mak K F, Lee C G, Hone J, et al. Atomically thin MoS₂: A new direct-gap semiconductor. Phys Rev Lett, 2010, 105, 136805 doi: 10.1103/PhysRevLett.105.136805
[6]	Li X L, Han W P, Wu J B, et al. Layer-number dependent optical properties of 2D materials and their application for thickness determination. Adv Funct Mater, 2017, 27(19), 1604468 doi: 10.1002/adfm.201604468
[7]	Wu J B, Zhang X Z, Ijäs M, et al. Resonant Raman spectroscopy of twisted multilayer graphene. Nat Commun, 2014, 5, 5309 doi: 10.1038/ncomms6309
[8]	Wu J B, Hu Z X, Zhang X, et al. Interface coupling in twisted multilayer graphene by resonant Raman spectroscopy of layer breathing modes. ACS Nano, 2015, 9(7), 7440 doi: 10.1021/acsnano.5b02502
[9]	Wu J B, Lin M L, Cong X, et al. Raman spectroscopy of graphene-based materials and its applications in related devices. Chem Soc Rev, 2018, 47(5), 1822 doi: 10.1039/C6CS00915H
[10]	Liu Y, Huang Y, Duan X F. Van der Waals integration before and beyond twodimensional materials. Nature, 2019, 567(7748), 323 doi: 10.1038/s41586-019-1013-x
[11]	Novoselov K S, Mishchenko A, Carvalho A, et al. 2D materials and van der Waals heterostructures. Science, 2016, 353(6298), aac9439 doi: 10.1126/science.aac9439
[12]	Geim A K, Grigorieva I V. Van der Waals heterostructures. Nature, 2013, 499(7459), 419 doi: 10.1038/nature12385
[13]	Lin M L, Tan Q H, Wu J B, et al. Moiré phonons in twisted bilayer MoS₂. ACS Nano, 2018, 12(8), 8770 doi: 10.1021/acsnano.8b05006
[14]	Yu H Y, Liu G B, Tang J J. Moiré excitons: From programmable quantum emitter arrays to spin-orbit-coupled artificial lattices. Sci Adv, 2017, 3(11), e1701696 doi: 10.1126/sciadv.1701696
[15]	Seyler K L, Rivera P, Yu H Y, et al. Signatures of moiré-trapped valley excitons in MoSe₂/WSe₂ heterobilayers. Nature, 2019, 567(7746), 66 doi: 10.1038/s41586-019-0957-1
[16]	Tran K, Moody G, Wu F C, et al. Evidence for moiré excitons in van der Waals heterostructures. Nature, 2019, 567(7746), 71 doi: 10.1038/s41586-019-0975-z
[17]	Jin C H, Regan E C, Yan A M, et al. Observation of moiré excitons in WSe₂/WS₂ heterostructure superlattices. Nature, 2019, 567(7746), 76 doi: 10.1038/s41586-019-0976-y
[18]	Zhou Z Q, Cui Y, Tan P H, et al. Optical and electrical properties of two-dimensional anisotropic materials. J Semicond, 2019, 40, 061001 doi: 10.1088/1674-4926/40/6/061001
[19]	Zhang X, Qiao X F, Shi W, et al. Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. Chem Soc Rev, 2015, 44(9), 2757 doi: 10.1039/C4CS00282B
[20]	Tan P H. Raman Spectroscopy of two-dimensional materials. Singapore: Springer, 2019
[21]	Liang L B, Zhang J, Sumpter B G, et al. Low-frequency shear and layer-breathing modes in raman scattering of twodimensional materials. ACS Nano, 2017, 11(12), 11777 doi: 10.1021/acsnano.7b06551
[22]	Tan P H, Han W P, Zhao W J, et al. The shear mode of multilayer graphene. Nat Mater, 2012, 11(4), 294 doi: 10.1038/nmat3245
[23]	Zhang X, Han W P, Wu J B, et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS₂. Phys Rev B, 2013, 87(11), 115413 doi: 10.1103/PhysRevB.87.115413
[24]	Lin M L, Zhou Y, Wu J B, et al. Cross-dimensional electron-phonon coupling in van der Waals heterostructures. Nat Commun, 2019, 10(1), 2419 doi: 10.1038/s41467-019-10400-z
[25]	Song Q J, Tan Q H, Zhang X, et al. Physical origin of davydov splitting and resonant Raman spectroscopy of davydov components in multilayer MoTe₂. Phys Rev B, 2016, 93(11), 115409 doi: 10.1103/PhysRevB.93.115409
[26]	Tan Q H, Zhang X, Luo X D, et al. Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings. J Semicond, 2017, 38(3), 031006 doi: 10.1088/1674-4926/38/3/031006
[27]	Wu J B, Wang H, Li X L, et al. Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition. Carbon, 2016, 110, 225 doi: 10.1016/j.carbon.2016.09.006
[28]	Lin M L, Chen T, Lu W, et al. Identifying the stacking order of multilayer graphene grown by chemical vapor deposition via Raman spectroscopy. J Raman Spectrosc, 2018, 49(1), 46 doi: 10.1002/jrs.5219
[29]	Li H, Wu J B, Ran F R, et al. Interfacial interactions in van der Waals heterostructures of MoS₂ and graphene. ACS Nano, 2017, 11(11), 11714 doi: 10.1021/acsnano.7b07015
[30]	Yang J H, Lee J U, Cheong H. Excitation energy dependence of Raman spectra of few-layer WS₂. FlatChem, 2017, 3, 64 doi: 10.1016/j.flatc.2017.06.001
[31]	Liang L B, Puretzky A A, Sumpter B G, et al. Interlayer bond polarizability model for stacking-dependent low-frequency Raman scattering in layered materials. Nanoscale, 2017, 9(40), 15340 doi: 10.1039/C7NR05839J

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Received: 06 August 2019 Revised: 16 August 2019 Online: Accepted Manuscript: 21 August 2019Uncorrected proof: 22 August 2019Published: 01 September 2019

Article Navigation > Journal of Semiconductors > 2019 > 40(9): 091001

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. doi: 10.1088/1674-4926/40/9/091001 ****X Cong, M L Lin, P H Tan, Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure[J]. J. Semicond., 2019, 40(9): 091001. doi: 10.1088/1674-4926/40/9/091001.

Citation:

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. doi: 10.1088/1674-4926/40/9/091001 ****

X Cong, M L Lin, P H Tan, Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure[J]. J. Semicond., 2019, 40(9): 091001. doi: 10.1088/1674-4926/40/9/091001.

Citation:

X Cong, M L Lin, P H Tan, Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure[J]. J. Semicond., 2019, 40(9): 091001. doi: 10.1088/1674-4926/40/9/091001.

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Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

DOI: 10.1088/1674-4926/40/9/091001

1.
State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
2.
Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Beijing Academy of Quantum Information Science, Beijing 100193, China

More Information

Corresponding author: E-mail: phtan@semi.ac.cn
Received Date: 2019-08-06
Revised Date: 2019-08-16
Published Date: 2019-09-01

Abstract

Abstract

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.
- two-dimensional materials,
- van der Waals heterostructure,
- Raman spectroscopy,
- lattice vibration,
- phonon

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References(31)

References

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306(5696), 666 doi: 10.1126/science.1102896
[2]	Fiori G, Bonaccorso F, Iannaccone G, et al. Electronics based on two-dimensional materials. Nat Nanotechnol, 2014, 9(10), 768 doi: 10.1038/nnano.2014.207
[3]	Mounet N, Gibertini M, Schwaller P, et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat Nanotechnol, 2018, 13(3), 246 doi: 10.1038/s41565-017-0035-5
[4]	Novoselov K S, Geim A K, Morozov S V, et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 2005, 438(7065), 197 doi: 10.1038/nature04233
[5]	Mak K F, Lee C G, Hone J, et al. Atomically thin MoS₂: A new direct-gap semiconductor. Phys Rev Lett, 2010, 105, 136805 doi: 10.1103/PhysRevLett.105.136805
[6]	Li X L, Han W P, Wu J B, et al. Layer-number dependent optical properties of 2D materials and their application for thickness determination. Adv Funct Mater, 2017, 27(19), 1604468 doi: 10.1002/adfm.201604468
[7]	Wu J B, Zhang X Z, Ijäs M, et al. Resonant Raman spectroscopy of twisted multilayer graphene. Nat Commun, 2014, 5, 5309 doi: 10.1038/ncomms6309
[8]	Wu J B, Hu Z X, Zhang X, et al. Interface coupling in twisted multilayer graphene by resonant Raman spectroscopy of layer breathing modes. ACS Nano, 2015, 9(7), 7440 doi: 10.1021/acsnano.5b02502
[9]	Wu J B, Lin M L, Cong X, et al. Raman spectroscopy of graphene-based materials and its applications in related devices. Chem Soc Rev, 2018, 47(5), 1822 doi: 10.1039/C6CS00915H
[10]	Liu Y, Huang Y, Duan X F. Van der Waals integration before and beyond twodimensional materials. Nature, 2019, 567(7748), 323 doi: 10.1038/s41586-019-1013-x
[11]	Novoselov K S, Mishchenko A, Carvalho A, et al. 2D materials and van der Waals heterostructures. Science, 2016, 353(6298), aac9439 doi: 10.1126/science.aac9439
[12]	Geim A K, Grigorieva I V. Van der Waals heterostructures. Nature, 2013, 499(7459), 419 doi: 10.1038/nature12385
[13]	Lin M L, Tan Q H, Wu J B, et al. Moiré phonons in twisted bilayer MoS₂. ACS Nano, 2018, 12(8), 8770 doi: 10.1021/acsnano.8b05006
[14]	Yu H Y, Liu G B, Tang J J. Moiré excitons: From programmable quantum emitter arrays to spin-orbit-coupled artificial lattices. Sci Adv, 2017, 3(11), e1701696 doi: 10.1126/sciadv.1701696
[15]	Seyler K L, Rivera P, Yu H Y, et al. Signatures of moiré-trapped valley excitons in MoSe₂/WSe₂ heterobilayers. Nature, 2019, 567(7746), 66 doi: 10.1038/s41586-019-0957-1
[16]	Tran K, Moody G, Wu F C, et al. Evidence for moiré excitons in van der Waals heterostructures. Nature, 2019, 567(7746), 71 doi: 10.1038/s41586-019-0975-z
[17]	Jin C H, Regan E C, Yan A M, et al. Observation of moiré excitons in WSe₂/WS₂ heterostructure superlattices. Nature, 2019, 567(7746), 76 doi: 10.1038/s41586-019-0976-y
[18]	Zhou Z Q, Cui Y, Tan P H, et al. Optical and electrical properties of two-dimensional anisotropic materials. J Semicond, 2019, 40, 061001 doi: 10.1088/1674-4926/40/6/061001
[19]	Zhang X, Qiao X F, Shi W, et al. Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. Chem Soc Rev, 2015, 44(9), 2757 doi: 10.1039/C4CS00282B
[20]	Tan P H. Raman Spectroscopy of two-dimensional materials. Singapore: Springer, 2019
[21]	Liang L B, Zhang J, Sumpter B G, et al. Low-frequency shear and layer-breathing modes in raman scattering of twodimensional materials. ACS Nano, 2017, 11(12), 11777 doi: 10.1021/acsnano.7b06551
[22]	Tan P H, Han W P, Zhao W J, et al. The shear mode of multilayer graphene. Nat Mater, 2012, 11(4), 294 doi: 10.1038/nmat3245
[23]	Zhang X, Han W P, Wu J B, et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS₂. Phys Rev B, 2013, 87(11), 115413 doi: 10.1103/PhysRevB.87.115413
[24]	Lin M L, Zhou Y, Wu J B, et al. Cross-dimensional electron-phonon coupling in van der Waals heterostructures. Nat Commun, 2019, 10(1), 2419 doi: 10.1038/s41467-019-10400-z
[25]	Song Q J, Tan Q H, Zhang X, et al. Physical origin of davydov splitting and resonant Raman spectroscopy of davydov components in multilayer MoTe₂. Phys Rev B, 2016, 93(11), 115409 doi: 10.1103/PhysRevB.93.115409
[26]	Tan Q H, Zhang X, Luo X D, et al. Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings. J Semicond, 2017, 38(3), 031006 doi: 10.1088/1674-4926/38/3/031006
[27]	Wu J B, Wang H, Li X L, et al. Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition. Carbon, 2016, 110, 225 doi: 10.1016/j.carbon.2016.09.006
[28]	Lin M L, Chen T, Lu W, et al. Identifying the stacking order of multilayer graphene grown by chemical vapor deposition via Raman spectroscopy. J Raman Spectrosc, 2018, 49(1), 46 doi: 10.1002/jrs.5219
[29]	Li H, Wu J B, Ran F R, et al. Interfacial interactions in van der Waals heterostructures of MoS₂ and graphene. ACS Nano, 2017, 11(11), 11714 doi: 10.1021/acsnano.7b07015
[30]	Yang J H, Lee J U, Cheong H. Excitation energy dependence of Raman spectra of few-layer WS₂. FlatChem, 2017, 3, 64 doi: 10.1016/j.flatc.2017.06.001
[31]	Liang L B, Puretzky A A, Sumpter B G, et al. Interlayer bond polarizability model for stacking-dependent low-frequency Raman scattering in layered materials. Nanoscale, 2017, 9(40), 15340 doi: 10.1039/C7NR05839J

Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

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Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

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Lattice vibration and Raman scattering of two-dimensional van der Waals heterostructure

DOI: 10.1088/1674-4926/40/9/091001

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