Interlayer vibrational modes in few-quintuple-layer ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ two-dimensional crystals: Raman spectroscopy and first-principles studies

Interlayer vibrational modes in few-quintuple-layer ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ two-dimensional crystals: Raman spectroscopy and first-principles studies

Yanyuan Zhao, Xin Luo, Jun Zhang, Junxiong Wu, Xuxu Bai, Meixiao Wang, Jinfeng Jia, Hailin Peng, Zhongfan Liu, Su Ying Quek, and Qihua Xiong

Phys. Rev. B 90, 245428 – Published 23 December 2014

Abstract

Layered materials, such as graphite/graphene, boron nitride, transition metal dichalcogenides, represent materials in which reduced size, dimensionality, and symmetry play critical roles in their physical properties. Here, we report on a comprehensive investigation of the phonon properties in the topological insulator ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ two-dimensional (2D) crystals, with the combination of Raman spectroscopy, first-principles calculations, and group theory analysis. Low frequency $(< 30 c m^{- 1})$ interlayer vibrational modes are revealed in few-quintuple-layer (QL) $B i_{2} T e_{3} / B i_{2} S e_{3}$ 2D crystals, which are absent in the bulk crystal as a result of different symmetries. The experimentally observed interlayer shear and breathing mode frequencies both show blueshifts, with decreasing thickness in few-QL ${Bi}_{2} {Te}_{3}$ (down to 2QL) and ${Bi}_{2} {Se}_{3}$ (down to 1QL), in agreement with first-principles calculations and a linear chain model, from which the interlayer coupling force constants can be estimated. Besides, an intense ultralow $(< 12 c m^{- 1})$ frequency peak is observed in 2–4QL ${Bi}_{2} {Te}_{3}$ , which is tentatively attributed to a substrate-induced interface mode supported by a linear chain model analysis. The high frequency Raman peaks exhibit frequency shifts and broadening from 3D to 2D as a result of the phonon confinement effect. Our studies shed light on a general understanding of the influence of dimensionality and crystal symmetry on the phonon properties in layered materials.

Received 20 September 2014
Revised 19 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245428

Authors & Affiliations

Yanyuan Zhao^1,*, Xin Luo^2,5,*, Jun Zhang¹, Junxiong Wu³, Xuxu Bai⁴, Meixiao Wang⁴, Jinfeng Jia⁴, Hailin Peng³, Zhongfan Liu³, Su Ying Quek^2,5,†, and Qihua Xiong^1,6,†

¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
²Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
³Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences (BNLMS), College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
⁴Department of Physics, Key Laboratory of Artificial Structures and Quantum Control, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
⁵Department of Physics, Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore
⁶NOVITAS, Nanoelectronics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore

^*These authors contributed equally to this work.
^†Author to whom correspondence should be addressed: queksy@ihpc.a-star.edu.sg and Qihua@ntu.edu.sg

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Vol. 90, Iss. 24 — 15 December 2014

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Figure 1
Crystalline structure and Raman modes of ${Bi}_{2} {Te}_{3}$ . (a) Crystalline structure $(R \bar{3} m)$ of $B i_{2} T e_{3} / B i_{2} S e_{3}$ . The primitive unit cell is indicated by the polyhedron (black solid lines). The lattice vectors of the unit cell are shown as the arrows denoted by $b_{1}, b_{2}$ , and $b_{3}$ . (b) Displacement schematics of the Raman active vibrational modes in bulk $B i_{2} T e_{3} / B i_{2} S e_{3}$ . The symbols “+” and “−” stand for vibrating perpendicularly to the paper, inward and outward, respectively. (c) Stokes and anti-Stokes Raman spectra of 3QL ${Bi}_{2} {Te}_{3}$ nanoplates on $Si O_{2} / Si$ substrates under both $z (x x) \bar{z}$ and $z (x y) \bar{z}$ polarization configurations in the high frequency region (top panel, $25 - 160 {cm}^{- 1})$ and low frequency region (bottom panel, $5 - 30 {cm}^{- 1})$ .
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Figure 2
Optical and AFM images of ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ 2D crystals grown through a vapor transport method. (a) Optical images of 2–4QL ${Bi}_{2} {Te}_{3}$ nanoplates grown on $Si O_{2} / Si$ substrates. The scale bar is 5 µm. (b) and (c) Optical images of 2–4QL ${Bi}_{2} {Te}_{3}$ and 1–5QL ${Bi}_{2} {Se}_{3}$ nanoplates grown on mica substrates. The scale bar is 10 µm. (d) and (f) AFM images of 2QL ${Bi}_{2} {Te}_{3}$ and 1–2QL ${Bi}_{2} {Se}_{3}$ nanoplates on mica. The inset thickness profiles are taken along the red dashed lines.
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Figure 3
Low frequency Raman spectrum evolutions as a function of QL number in ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ . (a) and (b) Low frequency Raman spectra of 2–11QL ${Bi}_{2} {Te}_{3}$ on $Si O_{2} / Si$ substrates measured using the (a) $\bar{z} (x x) z$ polarization configuration, and (b) the $\bar{z} (x y) z$ polarization configurations. (c) and (d) Low frequency Raman spectra of 1–7QL ${Bi}_{2} {Se}_{3}$ on mica substrates measured using the (c) $\bar{z} (x x) z$ polarization configuration and (d) the $\bar{z} (x y) z$ polarization configurations. The lowest frequency interlayer breathing, shear modes, and the out-of-plane interface phonon modes are denoted as B1, S1, and I, respectively, and their evolution trends are guided by the red, blue, and black dashed lines.
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Figure 4
Frequency evolutions of measured and computed interlayer shear, breathing, and interface modes in few-QL ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ , as well as and the linear chain model interpretation. (a) and (b) Plot of the lowest frequency shear (S1) and breathing (B1) mode frequencies as a function of QL number in few-QL (a) ${Bi}_{2} {Te}_{3}$ and (b) ${Bi}_{2} {Se}_{3}$ extracted from Fig. 3. The red solid (dashed) line is the fitting of the experimental (calculated) S1 modes versus thickness using the linear chain model. The blue solid (dashed) line is the fitting for the B1 modes using the same formula as for the S1 modes. (c) Comparison between the experimental and the calculated frequencies for the S1, B1, and I modes through the linear chain model with a substrate with $K_{i} / K = 0.5$ . (d) Schematics of the linear chain model. One blue sphere represents a QL. The force constant is $K$ between nearest-neighbor QLs, and the $K_{i}$ is the interface force constant between the ${Bi}_{2} {Te}_{3}$ nanoplate and the substrates. (e) and (f) Displacement schematics of the I, S1, and B1 modes in 2QL under the (e) free linear chain model and (f) linear chain model with a substrate. The arrows indicate the vibration directions of each QL, and the lengths are proportional to the displacement amplitudes.
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Figure 5
Substrate-dependent Raman spectra and force constant modeling of the I mode. (a) and (c) Low frequency Raman spectra of 2–4QL ${Bi}_{2} {Te}_{3}$ nanoplates grown on mica (blue dotted line) and $Si O_{2} / Si$ substrates (red dotted line). The black solid lines are fitted results through the multi-Lorentzian fitting, and the green lines are the Lorentzian peaks involved. The frequencies of the S1 and B1 modes do not show a substrate dependence, while that of the I mode largely depends on the substrates. (d) and (f) Calculated frequencies of the B1, S1, and I modes of 2–4QL ${Bi}_{2} {Te}_{3}$ on a substrate with the ratio of the interface and interlayer force constants $K_{i} / K$ varying from 0 to 3.
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Figure 6
Raman spectra of few-QL ${Bi}_{2} {Te}_{3}$ and analysis. (a) High frequency Stokes and anti-Stokes Raman spectra of bulk ${Bi}_{2} {Te}_{3}$ and 2–11QL nanoplates on $Si O_{2} / Si$ substrates. (b) and (c) Zoom-in view of the (b) $A_{1 g}^{1}$ and (c) $A_{1 g}^{2}$ peaks with varying thicknesses. (d) $A_{1 g}^{1}$ mode frequency versus nanoplate thickness. The red solid circles are experimental data and the blue solid squares are the calculated results. The calculated data are downshifted by $5.9 {cm}^{- 1}$ (blue open squares) to match the experimental bulk frequency. (e) $A_{1 g}^{2}$ mode frequency versus nanoplate thickness. The pink solid circles are experimental data, and the blue solid squares are the calculated results. The calculated data are upshifted by $2.6 {cm}^{- 1}$ (blue open squares) to match the experimental bulk frequency. (f) FWHM versus thickness of both $A_{1 g}^{1}$ and $A_{1 g}^{2}$ modes and the phenomenological fittings.
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Physical Review B

covering condensed matter and materials physics

Interlayer vibrational modes in few-quintuple-layer ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ two-dimensional crystals: Raman spectroscopy and first-principles studies

Yanyuan Zhao, Xin Luo, Jun Zhang, Junxiong Wu, Xuxu Bai, Meixiao Wang, Jinfeng Jia, Hailin Peng, Zhongfan Liu, Su Ying Quek, and Qihua Xiong

Phys. Rev. B 90, 245428 – Published 23 December 2014

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Physical Review B

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Interlayer vibrational modes in few-quintuple-layer Bi2Te3 and Bi2Se3 two-dimensional crystals: Raman spectroscopy and first-principles studies

Yanyuan Zhao, Xin Luo, Jun Zhang, Junxiong Wu, Xuxu Bai, Meixiao Wang, Jinfeng Jia, Hailin Peng, Zhongfan Liu, Su Ying Quek, and Qihua Xiong

Phys. Rev. B 90, 245428 – Published 23 December 2014

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Interlayer vibrational modes in few-quintuple-layer ${Bi}_{2} {Te}_{3}$ and ${Bi}_{2} {Se}_{3}$ two-dimensional crystals: Raman spectroscopy and first-principles studies