Polarized Raman spectra of phosphorene in edge and top view measuring configurations

Abstract

We demonstrate the anisotropic features of the A_1g, B_2g and A_2g vibrational Raman modes of phosphorene by performing for the first time a comparison of two orthogonal polarized Raman scattering studies in edge and top view measuring configurations. Despite the orthogonality between the vibration modes of A_1g and A_2g, they exhibit intense and very weak Raman intensities under light polarized along and transverse to the armchair edge, respectively, while the B_2g mode is virtually non-existent. The B_2g mode significantly appears only in the top view configuration. The studies performed under different intensities of excited light in the top view configuration are detailed for the sample rotated at 0°, 40°, 80° and 130° about the incident laser beam. The studies reveal a quadratic opposite behavior of the A_2g and B_2g modes and an unusual angle dependence of the A_1g vibrational mode. An unexpected behavior of the A_2g Raman mode at higher intensities, which still persists for the A_1g mode, is shown. The anomalous behavior of the A_1g mode from the edge and top view and the A_2g mode in the top view configuration is explained in terms of the layer stacking structures of phosphorene.

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Introduction

In recent years, black phosphorous, referred to currently as phosphorene, as a new 2D layered crystalline material with a varying band gap of 0.33 eV in bulk crystal and ∼1.88 eV in bilayers,^1–3 with a wrinkled structure along the armchair direction and a parallel arrangement of atoms in the zigzag direction, has drawn great interest both for theoretical and experimental investigations and is a promising material for various electronic and optoelectronic applications.⁴

Phosphorene, with a natural potential quality, can exceed the performance of crystal graphene layers due to interesting properties such as: (i) a high carrier mobility in the armchair direction, which is explained by a stronger coupling of the phosphorene layers;⁵ (ii) substantial anisotropic conducting features due to a unique ridge structure of the layers;⁶ (iii) a highly anisotropic band structure, depending on the number of layers and asymmetric optical behavior of phosphorene, which strongly absorbs light in the armchair rather than the zigzag direction; and (iv) thermal conduction, which is opposite to electrical conduction and is enhanced in the zigzag direction.⁷

One of the most important striking anisotropic features of phosphorene is its vibrational optical properties with respect to the internal electron displacement effect in terms of the induced molecular moment dipole. Raman scattering is an effective tool that can be successfully used to study the dependent vibrational modes (A_1g, B_2g and A_2g) that depend on the crystallographic orientation of a sample at different angles of rotation,⁸ the thickness of the sample,⁹ the temperature,¹⁰ different excitation wavelengths,^10,11 and the strain effect on Raman modes.¹² With regards to an established Cartesian reference system, it is well known that the Raman spectrum of phosphorene displays three vibration modes, i.e. A_1g, B_2g and A_2g, oriented orthogonally between them.^8,9,11 To complete this picture, in this paper, we focus on the anisotropic behavior of Raman signals in the edge and top view configurations as a function of two orthogonal polarizations of incident light. In the top view measurements, we analyze the dependence of the Raman spectra on the sample angle rotation (θ₁ = 0°, θ₂ = 40°, θ₃ = 80° and θ₄ = 130°) and proportion of the incident laser light to identify the orientation of the sample relative to the polarization directions of the excitation light, which highlights the anisotropic character of phosphorene and the anomalous trends of some vibrational modes and will be explained in terms of stacking-induced structural changes.

Experimental section

Materials

Phosphorene, as a bulk material formed into an agglomeration of microcrystals, was purchased from 2D Semiconductors Company, USA. By breaking the bulk state, microcrystalline structures with different orientations were obtained, from which lamellar particles of interest were selected via optical microscopic observation for observing the edge or flat sides. Starting from microscopic particles dispersed in dimethylformamide (DMF) and under intense sonication, a suspension of lamellar particles of different thickness is obtained, which, through drop-casting, was deposited onto a quartz support. From such structures deposited onto a quartz substrate, a planar particle was chosen, which subsequently was rotated about the normal to the surface with angles θ₁ = 0°, 40°, 80° and 130° relative to the longitudinal (L) and transverse (T) electric fields of the excitation laser light, which were kept at the same position every time.

Characterization

The Raman scattering in a back-scattering geometry was collected at room temperature (RT) using a 50× long work distance focusing objective with a Horiba Jobin-Yvon T64000 triple-grating spectrometer. Raman conducting trials in the polarized Raman light scattering were obtained under an excitation wavelength of 514.5 nm in two perpendicular polarizations of the laser excitation light using a rotating half-wave plate. In the case of the T64000 triple-grating spectrometer, to evaluate the intensities of different polarized Raman lines, certain precautions are required to optimize the maximum response of the grating dispersive system at different polarization of Raman lines. In this context, the highest and lowest efficiency is obtained under a light-polarized TM (transverse magnetic field) and TE (transverse electric field) respectively, i.e. when the Raman lines are polarized along or perpendicular to the grating groves, respectively. For a Raman spectrum containing polarized and un-polarized lines, the former can be detected with the highest efficiency in the TM configuration while the latter is detected in the TE configuration. In the latter case, TM optimal detection is achieved by rotating the polarization of Raman lines by means of a rotating half-wave blade interposed in the direction of the grating dispersive system, which ensures that the grating dispersive system analyses only one polarization state of light.

For this, it is also ensured that the grating dispersive system analyzed only one polarization state of light. The laser power of the samples was varied in proportions of 5, 10, 20, 50 and 100% from a maximum power of 0.2 mW, focused onto a 1.2 mm² spot. No thermal damage effects due to the laser excitation were observed in the samples.

Results and discussion

As in the case of a general layered crystal structure, when the atoms are arranged in repetitive rigid units characterized by strong intralayer bonds and weak interlayer van der Waals bonds along the z-direction,^13,14 phosphorene shows significant natural anisotropic optical,^8,10 mechanical¹⁵ and electrical⁴ properties, becoming a promising material for both basic research studies and various applications in optoelectronic fields and photonics. Similar to other layered materials, such as PbI₂,¹⁶ graphene,¹⁷ or different dichalcogenide materials, such as MoS₂ and WS₂,^18,19 phosphorene is expected to show a strong polarized Raman spectra dependence in the edge and top view configurations. Starting from these examples, a comprehensive study regarding the strongly anisotropic character of phosphorene in both the edge and top view configurations is conducted.

The identification of the crystalline structure in the zigzag and armchair directions of 2D phosphorene, correlated with the intuitive Cartesian coordinate axis, allows a schematic viewing of the vibrational modes A_1g, B_2g and A_2g, which are confirmed by Raman spectra. The most striking question is which one of the two edge configurations (zigzag or armchair) is the target of the incident laser light? The answer is given by the Raman spectra, more exactly by the different enhancement of the vibrational modes, which will be explained in the following.

The crystal structure orientation in the edge view of multi-layer phosphorene is shown in Fig. 1a, where the L-polarized light is along the X-axis, which coincides with the armchair direction, and the T-polarized light is oriented along the Z-axis. The X- and Y-axes are located in the plane of the layered top view arrangement, which corresponds to the T perpendicular polarized light. The typical Raman modes of phosphorene under two orthogonal polarizations L and T of the incident laser light of 514.5 nm, considering the armchair edge view of the layered phosphorene structure, are outlined in Fig. 1c. Considering at the beginning the in-plane A_2g vibrational mode behavior, the oscillation is activated and will give an important Raman signal when the orientation of the electric field corresponding to the L or T configurations coincides with the X-direction. In this case, the oscillation of the A_2g Raman mode is activated in the edge view configuration only by the optical electric field direction of the L-polarized laser light (black curve in Fig. 1c).

Fig. 1 (a) Armchair edge view configuration of phosphorene, adapted in a conventional crystallographic axis, where the directions for longitudinal (L) and transverse (T) polarization orientations of the excitation laser light are shown. In (b), the armchair edge configuration of phosphorene and the three ideal Raman vibration mode directions are outlined. In (c), the Raman spectra at room temperature (RT) are displayed for the edge view configuration under an incident excitation laser light of 514.5 nm (0.04 mW), with L-polarized light along the X-axis (black curve) and T-polarized light parallel to the Z-axis (red curve).

Evaluating the intensity ratio I_A2g(L)/I_A2g(T), one observes that the A_2g mode, located at 466 cm⁻¹, is ∼15 times more enhanced in the case of excitation light polarized along the layers (black curve) than in the transverse direction (red curve), which is consistent with the orientation of the crystalline structure of phosphorene relative to the optical electric field direction.

With respect to the A_1g vibrational mode situated at 362 cm⁻¹ with the intensity ratio I_A1g(L)/I_A1g(T) ∼ 15.74, Fig. 1c reveals an unexpected behavior in both polarizations, even though, according to the scheme from Fig. 1b, this mode should be activated only by T polarization light and the intensity ratio should be inverse. Note that an unexpected behavior of the A_1g Raman mode has also been observed in previous studies,^9,11,20 where the Raman tensors could not describe the vibrational mode dependence on the polarization directions of the incident light. On trying to understand this unique behavior, we note several details. Being an out-of-plane vibrational mode, the anomalous effect of A_1g with the direction in the growth c-axis of the embedded layers can be summarized considering the effects of stacking faults. The natural changes of the periodic atomic planar layers relative to one another due to the increase of entropy from strain induction is a general issue of the layered structures, which concerns central force potentials with a distortion impact on the natural behavior of the Raman modes. Therefore, the abnormal phenomenon arises because the vibrational direction of the out-of-plane A_1g Raman mode might not be perfectly vertical on the layer surface and thus the orthogonality condition between this mode and the other vibrational modes is no longer ensured.²¹ As in a natural layer-to-layer arrangement of the bulk structure, similar to any other 2D material,¹⁴ phosphorene exhibits layer stacking, with a strong influence on the electronic and optical properties (e.g. Raman scattering).^22,23 Specific to the stacking faults of the layered structure that influence the behavior of the in-plane vibration modes, we would expect a coupling contribution of the out-of-plane and in-plane oscillations of the A_1g mode, which displays a variation from an angle of 90° formed with the XY crystalline layer planes. In this context, the interference effects are predominant due to multiple reflection effects of the stacking faults and thus the optical response of the A_1g Raman mode in L-polarized light is enhanced, which would explain the similarity between the A_1g and A_2g intensities.⁹ Contrary to the A_1g and A_2g modes and according to expectations, the polarization dependence of the in-plane B_2g Raman mode at ∼439 cm⁻¹ in the armchair edge view configuration of phosphorene is less sensitive to both L- and T-polarized laser light.

The B_2g vibrational mode is also an in-plane Raman mode, but is orthogonal with the A_2g mode; in other words, its oscillations correspond to the Y-direction which coincides with the zigzag configuration of phosphorene. For this reason, in the armchair edge view configuration corresponding to the X-direction (Fig. 1b), the B_2g vibrational mode is almost inactive in both the L and T configurations, because it identifies the same direction with the spot of the incident laser light propagating along the Z-axis.

Considering the symmetric selection rule, the B_2g Raman mode should be detected only when the incident laser light is perpendicular to the sample layered structures, i.e. only in the top perspective view of the structure, when the incident laser light is along the Z-axis. Such behavior is further strengthened in Fig. 2 by measurements performed on stacked layers that offer combined results from the zigzag edge and top view configurations, the latter being optimized also for the signature of B_2g.

Fig. 2 (a) Optical microscopy image of stacked phosphorene layers, which allow for Raman spectra to be obtained in two simultaneous configurations, i.e. zigzag edge and top view, under orthogonally polarized laser excitation light, i.e. L and T. (b) Crystal structure scheme of the top layer of stacked phosphorene layers and its A_1g, B_2g and A_2g vibrational modes. (c) Polarized Raman spectra at RT for excitation laser light of 514.5 nm (0.04 mW) for the stacked phosphorene layers for L (black curve) and T (red curve).

Similar to ref. 9 and 24, the identification of the crystalline structure in the three-dimensional space shown in Fig. 2b, correlated with the intuitive Cartesian coordinate axis, allows schematic viewing of the vibrational modes A_1g, B_2g and A_2g, which are confirmed by the Raman spectra shown in Fig. 2c. It is important to note that the most suggestive Raman mode for understanding the crystal structure orientation of phosphorene in the edge configurations is B_2g. As is observed, there is no signal in Fig. 1c in both the L and T configurations. This is true when the oscillation of B_2g does not follow the direction of the L and T configurations, which is valuable only in the armchair configuration (Fig. 1b). So as it can be seen, this Raman mode can be activated when the electric field is along the Y-direction, namely in the zigzag direction, which is consistent with Fig. 2b, where B_2g is activated by the T-polarized light. As expected, Fig. 2c highlights a very low intensity of the A_1g Raman mode, because in this case, the movement of the atoms out of the XY plane does not coincide with the L and T polarization directions of light.

Note that the intensity of the A_2g mode in the zigzag edge configuration (∼4200 counts) shown in Fig. 2c is higher with regards to the result revealed in Fig. 1c in the armchair configuration, where the A_2g mode had ∼3000 counts. These explanations are given in terms of anisotropic reflectance changes depending on the edge-type structure configuration and are a consequence to identify the zigzag and armchair configurations. According to a theoretical prediction,⁹ the difference in magnitude of the A_2g mode is emphasized by the calculated interference enhancement factor, which predicts a higher enhancement of the Raman mode in the zigzag rather than in the armchair configuration. Therefore, we expect that different staking effects in both the armchair direction (X-axis) and zigzag direction (Y-axis) determine the highly anisotropic reflection and interference of light with different intensities of the A_2g line.

These arguments were also made by Wang et al.,²⁵ who predicted a flexible buckling curvature along the armchair direction and a breaking structure of phosphorene in the zigzag direction under a large uniaxial compressive strain applied along both the X- and Y-axis. Therefore, the stacking disorder response in the armchair direction is more probable and thus the decrease in intensity of the oscillation strength is attributed to the relaxation momentum of the A_2g scattering phonon caused by various types of stacking effects.²⁶

Specific to a 2D structure, the edge view polarized Raman spectra are refined in new detail in the top view studies. In this context, to explore the different signatures of the combined armchair and zigzag crystalline directions, Fig. 3 reveals Raman studies under an excitation laser light of 514.5 nm in the top view configuration, performed under L and T polarization of the excitation light, for the same sample as in the case of the edge view, but rotated counter clockwise at different angles (0°, 40°, 80°, and 130°, denoted as Q₁, Q₂, Q₃ and Q₄) relative to the L and T directions, which are kept in the same initial position every time.

Fig. 3 (a) Optical microscopy illustration of a plate sample chosen in the XY plane view, which was rotated around the yellow dot that denotes also the spot of the incident laser light propagating along the Z-axis; (b) the scheme of the crystalline structure of phosphorene in the top view configuration in the XY plane, with L and T denoting the directions of the polarized laser light along the armchair and zigzag configurations; and (c) the sample rotation angle at θ₁ = 0°, 40°, 80° and 130° relative to the orientation of the L and T electric field directions.

The dichroic property of phosphorene indicated by the anisotropic conductivity in the armchair and zigzag directions and the sensitivity of the absorbance under rotated polarized light was evidenced in ref. 27–29. New significant details regarding the polarized Raman spectra of this materials are still disclosed in Fig. 4, when the spectra were recorded at an intensity of the incident laser light of 20%, as follows:

Fig. 4 Raman spectra in the top view of phosphorene under the excitation laser light of 514.5 nm (0.04 mW) at RT at different in-plane angles of rotation of the sample: θ₁ = 0° (sample Q₁, (a)), θ₂ = 40° (sample Q₂, (b)), θ₃ = 80° (sample Q₃, (c)), and θ₄ = 130° (sample Q₄, (d)). For highlighting the optical anisotropy of the sample, the measurements are done in two experimental configurations of the polarized laser light: L (black curve) and T (red curve).

(i) The interaction of light with phosphorene would imply less possible oscillation strength of the A_1g vibrational mode when the orientation of the sample is considered in the top view configuration. However, the question that arises is this: how can this unusual phenomenon be explained when such behavior is possible? Similar to Fig. 1b, where A_1g is abnormally enhanced in the L polarization light in the edge view configuration, one observes in Fig. 4 an unusual behavior of the Raman scattering depicted by the A_1g vibrational mode in both the L and T polarizations. Through a deep analysis of the vibration eigenvectors,²¹ the coupling of the out-of-plane and in-plane oscillations of a vibrational mode of A_1g is the outstanding reason for such anomalies. In this circumstance, the oscillators couple fully or partially with the electric field, depending on the degree of flattening of the vibration mode, and give an enhanced Raman response that can be observed even in the top view configuration.

(ii) At θ₁ = 0°, i.e. for sample Q₁, where the L and T polarizations are oriented along the armchair and zigzag directions, Fig. 4a indicates a higher intensity of A_2g and B_2g for L and T, respectively, with I_A2g(L)/I_A2g(T) ∼ 17 and I_B2g(T)/I_B2g(L) ∼ 16, due to the condition of orthogonality established between the two vibrational Raman modes.

(iii) In Fig. 4b, i.e. the Raman spectrum at θ₂ = 40° (sample Q₂), mixing signals collected from both the armchair and zigzag directions are shown, where the intensities in the L and T electric field directions are decreased and manifest approximately equally in both A_2g and B_2g.

(iv) The sample rotated at θ₃ = 80° gives the Raman spectra in Fig. 4c, where the intensities of the A_2g and B_2g lines are increased again but in a different manner compared with the case of Q₁. Opposite to the θ₁ = 0° situation, the signals recorded for the armchair direction are attributed to the A_2g mode, which manifest greater enhanced Raman lines for T-polarized light, while the signal recorded for the zigzag direction is associated with the B_2g mode, which has a greater intensity in the L polarization of light.

(v) In Fig. 4d, for sample Q₄ at θ₃ = 130°, the B_2g and A_2g Raman lines behave similarly under L and T polarization, with the signal being collected from both the armchair and zigzag directions, as in the case of sample Q₂.

Another summary of the above results is displayed in Fig. 5, which highlights that the A_2g and B_2g Raman modes show a quadratic dependence on the sample rotation angle with an inverse parabola depending on the L and T polarization configurations. With regards to Fig. 3, where the A_1g Raman line at 362 cm⁻¹ is associated with an out-of-plane vibrational mode, one observes that regardless of the rotation angle used, it seems to be invariant to a periodic variation relative to L and T polarizations of excitation light, with an increasing intensity towards higher rotation angles of the sample. This abnormal behavior was also observed in edge view measurements and is similar with that highlighted in ref. 9–11. The results shown in Fig. 5a and b are in accordance with the calculated intensity of polarized Raman signals with respect to the Raman tensors in the back-scattering geometry developed in ref. 9,10,24,30, where the A_2g and B_2g modes have a sine and cosine variation with I_∥ ∼ d² sin² 2θ and I_⊥ ∼ d² cos² 2θ for the parallel and perpendicular polarizations. This indicates an opposite quadratic variation, as observed in Fig. 5a and b, in which d is a parameter related to the laser excitation intensity.

Fig. 5 Raman intensity dependence of sample rotation angle in the three Raman modes: (a) A_2g; (b) B_2g; and (c) A_1g in both polarized light configurations under an excitation laser light of 514.5 nm and at a proportion of light intensity of 20%.

Regarding the out-of-plane Raman mode A_1g, it highlights an increase in intensity due to the change in L and T polarizations of excitation light and should be explained by the coupled out-of-plane and in-plane oscillations, with a larger component signal in the L-polarized direction, which depends on the local stacking faults of the material, as is described in detail earlier.

Note that the anomalous polarization dependence of the Raman intensity has recently been revealed and has a dependence on the thickness of the sample originating in the interference effect due to the dichroic and birefringence character inside the layered structure of phosphorene,⁹ a dependence on the temperature,¹⁰ and a dependence on the variation of excitation wavelengths.^9,11 In this context, another question arises: does the polarization state of the vibrational Raman modes depend on the intensity of the excitation laser light, which is expected to be linked to the unequal absorption of light along the armchair and zigzag crystalline axes? In what follows, the variation of the A_2g and B_2g lines due to the L and T polarization state is studied in the top view measuring configuration under different intensities of an incident excitation laser of 514.5 nm in the range of 5, 20, 50 and 100% from a power of 0.2 mW. Note that the A_1g mode isn’t relevant and is not shown and explored here, having similar abnormal variation no matter the proportion of the intensity.

Such dependence is highlighted in Fig. 6, which reveals the following significant details: (i) the B_2g Raman line intensity varies in opposition to a rotated angle of 80°, similar to what could be obtained at 90°, from the maximum and minimum intensity in L and T, which is shown in Fig. 6a and b, respectively. These results are very consistent with the calculated Raman tensors of B_2g,^8,9,24 from which I_∥ ∼ d² sin² 2θ and I_⊥ ∼ d² cos² 2θ, where d is a parameter proportional to the intensity of the incident laser light; (ii) the T polarization dependence of the A_2g mode, illustrated in Fig. 6d, has a natural and specific quadratic behavior, in opposition to the Raman signal intensities of B_2g in L polarization light, due to the orthogonality of the two vibrational directions; and (iii) despite expectations, Fig. 6c, showing an L polarization dependence of the A_2g Raman line intensity, should show a variation with the laser excitation intensity similar to that presented for B_2g in T-polarized light (Fig. 6b), this being a consequence of their orthogonality.

Fig. 6 Angular dependence of the Raman intensities of B_2g and A_2g under an excitation laser light of 514.5 nm at different intensities, i.e. 5% black, 20% red, 50% blue, and 100% green, from 0.2 mW under L (a and c) and T (b and d) polarizations of light.

Actually, Fig. 6c reveals two types of variation of the A_2g mode with the excitation laser intensity: a weaker one at low excitation intensities (5% and 20%) that is similar to that of B_2g from Fig. 6c, and another one, which is abnormal, that occurs at higher excitation intensities (50% and 100%).

This different behavior of the A_2g and B_2g modes is related to the movements of atoms along the armchair and zigzag directions, respectively, as shown in Fig. 3b. For a layered structure, the stacking faults, which influence the supplementary in-plane vibrational modes, also play a major role, as shown in Fig. 3b. In this case, the anisotropic character of phosphorene along the zigzag and armchair directions,^5–7 as proven by the ease of destruction in the armchair direction,²⁶ combined with the stacking faults in a layered structure, originates from the abnormal behavior of A_2g. Note that the abnormal behavior of the A_2g Raman mode of phosphorene is similar to the behavior of the E_2g mode in MoS₂ and WS₂,^18,19 whose explanations are based on the stacking faults effect.

Conclusions

In this paper, we present new and unique experimental data of polarized Raman scattering performed in back-scattering geometry for bulk phosphorene in the edge and top view configurations of a sample. Raman spectra are investigated alternatively in two orthogonal polarizations, i.e. L and T, of incident laser light, from which new features of the vibration modes of phosphorene are revealed.

The primary results illustrated in this study are as follows.

(i) The Raman signals in the armchair and zigzag edge view directions are different and depend on the parallel and perpendicular configurations of the polarized incident light. From the armchair edge view, the A_1g and A_2g vibration modes are strongly enhanced under L-polarized incident light, while B_2g is less sensitive to both L and T electric field directions. The abnormally high enhancement of the A_1g mode is interpreted in terms of both coupled out-of-plane and in-plane vibrations due to the stacking faults effect. In the zigzag edge view, the Raman signal is recorded for both the edge and top configurations, denoting a great magnitude of the B_2g mode and a very low intensity of the A_1g Raman mode, with normal behaviors according to the electric field directions. The greater intensity of the Raman signals in the zigzag edge compared with the armchair configuration is explained by considering the greater flexibility of the staking faults in the armchair direction, which makes it susceptible also to different optoelectronic applications.

(ii) In the top view measuring configuration, by rotating the sample at different angles relative to the L and T configurations, a quadratic dependence of the A_2g and B_2g modes on both the L and T polarizations of excitation light is revealed, while the A_1g Raman mode behaves abnormally. The anomalous enhancement of the A_1g line in the top view configuration is interpreted as the result of mode coupling associated with the out-of-plane and in-plane vibration modes. The anisotropy of the phosphorene crystal structure is also illustrated by the polarization dependence of Raman signals on different intensities of power of incident light (5, 20, 50 and 100%) in both the L and T configurations. The dependence could be explained in terms of the stacking-induced anisotropic structure of phosphorene, where the A_2g vibration mode behaves abnormally.

Acknowledgements

This work was financially supported by the Romanian National Agency for Scientific Research and Innovation, project no. PN 16-480102.

Notes and references

1. L. K. Li, Y. J. Yu, G. J. Ye, Q. Q. Ge, X. D. Ou, H. Wu, D. L. Feng, X. H. Chen and Y. B. Zhang, Nat. Nanotechnol., 2014, 9, 372.
2. A. H. Woomer, T. W. Farnsworth, J. Hu, R. A. Wells, C. L. Donley and S. C. Warren, ACS Nano, 2015, 9, 8869.
3. X. M. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. C. Jia, H. Zhao, H. Wang, L. Yang, X. D. Xu and F. N. Xia, Nat. Nanotechnol., 2015, 10, 517.
4. L. Kou, C. Chen and S. C. Smith, J. Phys. Chem. Lett., 2015, 6, 2794.
5. J. Qiao, X. Kong, Z.-X. Hu, F. Yang and W. Ji, Nat. Commun., 2014, 5, 4475.
6. H. Liu, A. T. Neal, Z. Z. Luo, D. Tomanek and P. D. Ye, ACS Nano, 2014, 8, 4033.
7. R. Fei, A. Faghaninia, R. Soklaski, J.-A. Yan, C. Lo and L. Yang, Nano Lett., 2014, 14, 6393.
8. J. Wu, N. Mao, L. Xie, H. Xu and J. Zhang, Angew. Chem., Int. Ed., 2015, 54, 2366.
9. J. Kim, J.-U. Lee, H. J. Park, Z. Lee, C. Lee and H. Cheong, Nanoscale, 2015, 7, 18708.
10. S. Zhang, J. Yang, R. Xu, F. Wang, W. Li, M. Ghufran, Y.-W. Zhang, Z. Yu, G. Zhang, Q. Qin and Y. Lu, ACS Nano, 2014, 8, 9590.
11. H. B. Ribeiro, M. A. Pimenta, C. J. S. de Matos, R. L. Moreira, A. S. Rodin, J. D. Zapata, E. A. T. de Souza and A. H. C. Neto, ACS Nano, 2015, 4, 4270.
12. R. Fei and L. Yang, Appl. Phys. Lett., 2014, 105, 083120.
13. J. A. Wilson and A. D. Yoffe, Adv. Phys., 1969, 18, 193.
14. P. A. Beckmann, Cryst. Res. Technol., 2010, 45(5), 455.
15. O. Wei and X. Peng, Appl. Phys. Lett., 2014, 104, 251915.
16. M. Baibarac, I. Smaranda, M. Scocioreanu, R. A. Mitran, M. Enculescu, M. Galatanu and I. Baltog, Mater. Res. Bull., 2015, 70, 762.
17. A. K. Gupta, T. J. Russin, H. R. Gutiérrez and P. C. Eklund, ACS Nano, 2009, 3, 45.
18. C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone and S. Ryu, ACS Nano, 2010, 4, 2695.
19. A. Molina-Sanchez and L. Wirtz, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 84, 155413.
20. Z. Guo, H. Zhang, S. Lu, Z. Wang, S. Tang, J. Shao, Z. Sun, H. Xie, H. Wang, X.-F. Yu and P. K. Chu, Adv. Funct. Mater., 2015, 25, 6996.
21. Y. Feng, J. Zhou, Y. Du, F. Miao, C.-G. Duan, B. Wang and X. Wan, J. Phys.: Condens. Matter, 2015, 27, 185302.
22. J. Dai and X. C. Zeng, J. Phys. Chem. Lett., 2014, 5, 1289.
23. A. Manjanath, A. Samanta, T. Pandey and A. K. Singh, Nanotechnology, 2015, 26, 075701.
24. J. Ribeiro-Soares, R. M. Almeida, L. G. Cacado, M. S. Dresselhause and A. Jorio, Phys. Rev. B: Condens. Matter, 2015, 91, 205421.
25. G. Wang, G. C. Loh, R. Pandey and S. Karna, Nanotechnology, 2016, 27, 05570.
26. T. Karasawa, T. Komatsu, K. Miyata, T. Iida and Y. Kaifu, Physica B+C, 1981, 105, 88.
27. V. Tran, R. Soklaski, Y. Liang and L. Yang, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 235319.
28. T. Low, A. S. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia and A. H. Castro Neto, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 90, 075434.
29. J. He, D. He, Y. Wang, Q. Cui, M. Z. Bellus, H.-Y. Chiu and H. Zhao, ACS Nano, 2015, 9, 6436.
30. M. I. Aroyo, J. M. Prerez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov and H. Qondratschek, Z. Kristallogr., 2006, 221, 12.

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