Polarized Nonresonant Raman Spectra of Graphene Nanoribbons

ARTICLE pubs.acs.org/JPCC

Polarized Nonresonant Raman Spectra of Graphene Nanoribbons Guangfu Luo,†,‡,§ Lu Wang,§ Hong Li,† Rui Qin,† Jing Zhou,† Linze Li,† Zhengxiang Gao,† Wai-Ning Mei,§ Jing Lu,*,† and Shigeru Nagase*,‡ †

State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, People’s Republic of China Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan § Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266, United States ‡

bS Supporting Information ABSTRACT: We study the nonresonant Raman scattering of armchair and zigzag graphene nanoribbons (GNRs) using density functional perturbation theory. We find that, in both GNR types, the Raman spectrum is extremely polarized along the ribbon axis direction with the scattering intensity being over 102 times greater than those of the other polarizations because of the geometrical confinement. Along the dominant polarization direction, the scattering intensity and frequency oscillate strongly with the ribbon width in the armchair GNRs, while the scattering intensity initially increases and then decreases with the ribbon width and the frequency monotonically changes with the ribbon width in the zigzag GNRs. Such a difference is closely associated with the different width dependences of band structure between the two types of GNRs.

’ INTRODUCTION Ever since their first fabrications, the single-atom-thick graphene and graphene nanoribbons (GNRs) have attracted a huge amount of attention because of their peculiar behaviors and great potential in the next-generation electronics.1
4 Electronic optical absorption, infrared (IR), and Raman spectroscopy are three broadly utilized characterization techniques of nanostructures because of their accessible, fast, nondestructive, and large-area detection advantages. Resonant Raman spectroscopy (RRS) is especially extensively used to identify the graphene edges,5,6 layer number,7,8 and polarization feature.9,10 In addition, surfaceenhanced Raman spectroscopy (SERS) and tip-enhanced Raman spectroscopy (TERS) recently have also been applied in the study of graphene,11,12 enriching the experimental tools for graphenerelated studies. Contrary to the wide experimental applications, theoretical studies of Raman spectra of GNRs are limited to the nonresonant Raman spectrum level and utilize the empirical bond-polarization model. Among them, Zhou et al.13 found three typical modes in GNRs: first, a breathing mode similar to that in the carbon nanotube; second, a mode similar to the E2g mode in graphene; and third, an edge vibrational mode. Malola et al.14 studied the influences of the edge structure of GNRs and discovered an edgerelated Raman peak. Saito et al.15 found that the vibrational modes are symmetry-selective under different polarizations in some bare-edge GNRs. It should be pointed out that the empirical bond-polarization model16,17 expresses the static electronic polarizability of a system as a sum of individual bond polarizability, which naturally ignores the influences of chemical environment, and assumes a cylindrical symmetry around the principal axis of r 2011 American Chemical Society

the chemical bonds. Hence, a first-principles study of the Raman spectra of GNRs is desirable to acquire more reliable results. Recently, we performed a comprehensive investigation on the polarized vibrational IR spectra of edge-hydrogenated GNRs through first-principles calculations and revealed several features, such as a width-insensitive peak originating from an edge wagging mode and noticeable spectral differences between two GNR types.18 In view of the complementary relationship between IR and Raman spectroscopies and other aforementioned reasons, in this paper, we present an extensive first-principles study on the nonresonant Raman spectra of the edge-hydrogenated GNRs. We uncover, for example, a very strong polarization effect along the ribbon axis direction, a much larger difference between the GNR types, and a very weak Raman scattering by the edge vibrational modes. We also propose a possibility of testing our nonresonant Raman spectra by using SERS and TERS.

’ MODEL AND METHOD As shown in Figure 1, we consider two types of GNRs: the armchair (zigzag) GNR with m number of C
C dimers (zigzag carbon chains) across the ribbon width direction is denoted as mAGNR (m-ZGNR). We examine the AGNRs with m from 8 to 19 and ZGNRs with m from 5 to 12. In the ZGNRs, we consider the antiferromagnetic ground state. All calculations are carried out under density functional perturbation theory (DFPT) within the local (spin) density approximation as implemented in the Received: March 28, 2011 Revised: October 7, 2011 Published: November 10, 2011 24463

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Figure 1. Schematic structures of an 8-AGNR (left) and a 5-ZGNR (right). The Cartesian coordinates and the ribbon width are indicated.

ABINIT code.19,20 A plane-wave energy cutoff of 600 eV and norm-conserving pseudopotentials are employed. Periodic boundaries are used, and the nearest atom distance between neighbor cells is 10 Å. Uniform 1  1  12 and 1  1  24 k-point grids are adopted for the Brillouin zone sampling of the AGNRs and ZGNRs, respectively. The maximum force tolerance is 10
4 eV/Å in the full geometrical optimizations. The Raman scattering cross section of the Stokes part per unit cell is defined as21 dσ m ðω0
ωm Þ4 p ¼ V0 jes 3 αm 3 e0 j2 ðnm þ 1Þ 2 4 2ω dΩ ð4πÞ c m pffiffiffiffiffi ∂χ Um αm ¼ V0 ∂τ

∑

ð1Þ

Therein V0 is the unit cell volume, ω0 and ωm are, respectively, the frequencies of the incident light and the mth vibrational mode; es and e0 are the polarization directions of the scattering and incident light, respectively; αm is the Raman susceptibility tensor, and nm the Bose
Einstein distribution; ∂χ/∂τ is the firstorder change of the linear dielectric susceptibility tensor χ with respect to an atomic displacement τ, and finally Um is the eigenvector of this vibration. Since ω0 . ωm is satisfied in most experiments, then (ω0
ωm)4 ≈ ω40 is considered as a constant in our calculations. To guide the eye, we broaden each Raman peak to a Lorentzian line shape with a 20 cm
1 line width.

’ RESULTS AND DISCUSSION As a typical case, we present the first three strongest Raman spectra of the 18-AGNR and 10-ZGNR, respectively, in panels a and b of Figure 2. The first noticeable feature we observe is the strong anisotropy of the Raman intensity, a phenomenon absent in their IR spectra.18 The Raman spectrum for the ZZ polarization possesses the greatest intensity, over 103 and 102 times greater than those of the second greatest polarization for the 18AGNR and 10-ZGNR, respectively. This strong anisotropy is generally available for other GNRs and is attributed primarily to the geometrical confinement effect—namely, the electrons are localized in the out-of-plane (x) and ribbon width (y) directions while free in the ribbon axis direction (z). Thus, the electron cloud is much more easily to be distorted when an external electric field is polarized along the z direction, and consequently, the Raman susceptibility is much greater and renders a much higher scattering intensity compared with other polarizations. Actually, the above phenomenon, called “antenna effect”, has been observed in the RRS experiments of single-walled carbon nanotubes,22 WS2 nanotube,23 GaN nanwire,24 GaP nanowire,25,26

Figure 2. Three strongest Raman spectra of an (a) 18-AGNR and (b) a 10-ZGNR. The numbers on the top-left corners are scale factors for the ZZ polarizations, where the first and second letters correspond to the polarization directions of the incident and scattering light, respectively. Insets are the amplified spectra of the C
H vibrational modes at the frequencies indicated by the arrows. The E2g-like peaks in both GNR types are labeled. (c) Vibrational modes and Raman susceptibility of all atom contribution for the peaks α, β, and γ in the 18-AGNR. The spot size is proportional to the magnitude of Raman susceptibility, while the different colors (red and blue) represent opposite signs. For easy visualization, the spot sizes for the peak γ are amplified by 30-fold relative to those of the peak α or β.

and GNRs.10 Hereafter, we shall focus on the ZZ polarization for all Raman spectra. In both GNR types, we find a major peak around 1580 cm
1 (Figure 2), which resembles the E2g mode of graphene in both frequency (1588 cm
1) and vibrational mode. Our later analyses, however, show that the E2g-like modes in the two GNR types display quite different ribbon width dependences: in the AGNRs, the peak oscillates substantially with the ribbon width, but in the ZGNRs, it varies gradually with the ribbon width. Another difference between the two GNR types is that there are two additional prominent Raman peaks (labeled as α and β) around 24464

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Figure 3. (a) Raman spectra of the m-AGNR (m = 9
17) for the ZZ polarization. Intensity of the m = 3p + 2 category is reduced by 10
3 times (shaded area). (b) Left: Width dependence of the E2g-like mode around 1568 cm
1 (m = 8
19). Right: Vibrational modes and Raman susceptibility of all atom contribution for the peaks α, β, and γ. For easy visualization, the spot sizes for the peaks α and β have been, respectively, amplified by 16.2 and 86.8 times relative to those of the peak γ. The frequency of the E2g mode in graphene, 1588 cm
1, and its Raman intensity with the same carbon atoms as the mAGNR in each unit cell are indicated with dashed lines.

1300 cm
1 besides the major Raman scattering peak in the AGNRs. This spectral difference is robust and can be employed as a useful character to distinguish between the AGNR and ZGNR. The vibrational modes and Raman susceptibility of atom contribution for the peaks α and β of the 18-AGNR are shown in Figure 2c. Unlike the IR spectra of GNRs,18 we do not observe obvious Raman scattering of the local C
H vibrational modes, though several of them are, in principle, Raman-active. For example, the C
H stretching mode in the 18-AGNR (peak γ in Figure 2a) is located at 3015 cm
1, and its Raman susceptibility is ∼46 times lower than that of the peak α (Figure 2c). The little contribution of the C
H vibration is also seen from the Raman susceptibility of each atom for the peaks α and β (Figure 2c). We attribute such low Raman intensities to the high polarity of the C
H bond, which is much harder to be altered than the delocalized π electron system. Another striking feature is the prominent family dependence of the Raman spectra in the AGNRs. As shown in Figure 3a, the Raman spectra of the AGNRs can be clearly classified into three categories: the 3p-AGNR, (3p+1)-AGNR, and (3p+2)-AGNR, where p is a positive integer. A similar family dependence is also found earlier in the vibrational IR spectra.18 However, the difference of the Raman intensity among families is much larger than that of the IR intensity: the highest Raman peak in the (3p+2)-AGNR is over 2  102 times stronger than those of the 3p-AGNR and (3p+1)-AGNR with a similar width, while the highest IR peak is just over several times greater than the second

highest.18 Interestingly, the Raman intensity order is just contrary to the band gap order in the AGNRs.27,28 In Figure 3b, we take the E2g-like mode as an example and show its Raman intensity and frequency variations with the ribbon width, together with the vibrational modes. With increasing ribbon width, the family differences gradually decrease and the Raman intensity and frequency converge to those of the E2g mode in graphene. To explore the underlying physics of the large intensity oscillation, we analyze the two components of Raman susceptibility, ∂χ/∂τ and Um, and find that the major difference comes from the former. Then we turn to an approximate way of deriving static dielectric function ε(0) and dielectric susceptibility χ because of the relationship ε = 1 + χ, the sum-over-states approach, which neglects the screening effect but is good enough to explain the above phenomenon. From the viewpoint of this method, the static dielectric function ε(0) satisfies the following Kramers
Kronig formula 2 Z ∞ ε2 ðωÞ dω ð2Þ εð0Þ ¼ 1 þ π 0 ω where ε2(ω), an odd function, is the imaginary part of ε(ω). Because of the 1/ω factor, the leading contribution to ε(0) comes from few low-energy peaks of ε2(ω)—in GNRs, it is the first one or two. Meanwhile, it is known that the first peak of ε2 in GNRs corresponds to the optical transition between bands that define the band gap. Therefore, χ and ∂χ/∂τ are closely related to the band gap,29 which is well-known for a three-period oscillation with the ribbon width.27,28 24465

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The Journal of Physical Chemistry C We further investigate the ε(0) variation with respect to a finite atomic displacement and reach the consistent conclusions with those from the Raman spectra (Figure S1, Supporting Information): (1) the smaller the band gap or the lower in energy the first peak of the ε2(ω)/ω spectrum, the stronger the Raman intensity; (2) (3p+2)-AGNR possesses much greater intensity than the other two GNR categories with a similar ribbon width. Actually, a quantitative analysis for the E2g-like mode shows that its Raman intensity is approximately proportional to the negative exponent of the AGNR band gap (Figure S2, Supporting Information). The relationship between the Raman intensity and band gap in an AGNR can also be qualitatively understood in terms of the perturbation theory:30 given other similar situations, an external electric field is easier to induce the π electron transition from the valence band to the conduction band when their energy difference (corresponding to the band gap of an AGNR) is smaller, and thus the Raman susceptibility is greater. Additionally, we notice that the ε2/ω spectrum of graphene is also characterized by a single strong peak (Figure S3, Supporting Information), and its energy is lower than or close to the band gaps the AGNRs (Table S1, Supporting Information). Therefore, the phenomenon that the Raman intensity of the E2g mode in graphene is greater than or similar to these of the E2g-like modes in the AGNRs is also explained in terms of the fact that the Raman intensity decreases with the band gap in the AGNRs. The Raman spectra of the ZGNRs for the ZZ polarization are shown in Figure 4a. By dashed lines, we connect the peaks that have similar vibrational modes and the same number of standing wave nodes n existing in the ribbon width direction. Contrary to the spectral oscillation with the ribbon width in the AGNRs, the Raman intensities roughly first increase (m < 7) and then decrease (m > 9) with the ribbon width. The frequencies generally change monotonically with the ribbon width in the ZGNRs: those with lower energy (1300 cm
1) increase with it. Taking the lowest peak in each spectrum (radial breathing-like mode (RBLM) as explained later) as an example, we show its intensity and frequency variations with the ribbon width in Figure 4b. The Raman intensity first increases with the ribbon width, peaking at the 7-ZGNR, and then decreases with the ribbon width; the corresponding Raman frequency decreases monotonically with the ribbon width. The ribbon width dependences of other peaks are similar and shown in Figure S4, Supporting Information. From the ε2/ω spectra of the ZGNRs, we find that the band gap or edge-state-related peak is still the major contribution to ε(0) (Figure S3, Supporting Information), but a smaller band gap does not necessarily lead to a higher ε2/ω peak and a greater Raman susceptibility because the band transition probability also becomes smaller. As an extreme example, when the ribbon width of a ZGNR increases to infinite, both its band gap and the related band transition probability vanish. From the standpoint of perturbation theory,30 such reverse contributions by the band gap and transition probability complicate the Raman susceptibility variation with the ribbon width in our examined range. However, when the ZGNR is wide enough, the edge-state-related peak becomes trifling and the second peak dominates the ε2/ω spectrum. Our calculations further show that the height of the second peak increases monotonically with the ribbon width (1.5
2.0 eV in Figure S3, Supporting Information). As a result, we expect that the ribbon width dependence of the Raman susceptibility increases monotonically in the wide ZGNR limit.

ARTICLE

Figure 4. (a) Raman spectra of the m-ZGNR (m = 5
12) for the ZZ polarization. Red dashed lines connect the peaks that have similar vibrational modes and the same number of standing wave nodes. The arrow indicates the frequency of the E2g mode in graphene, 1588 cm
1. The intensity below 950 cm
1 is amplified by 10-fold for all of the ZGNRs, and that from 1300 to 1700 cm
1 is reduced by 3, 2.5, and 1.5 times for the 6-, 7-, and 8-ZGNR, respectively. (b) Raman intensity and frequency variations with the ribbon width for the RBLM peak. (c) Vibrational modes and Raman susceptibility of all atom contribution for the peaks α, β, γ, and δ.

To understand the frequency versus ribbon width relationship in the ZGNRs, we map the frequencies of the Raman-active modes to the phonon dispersion of graphene as in the IR spectra18 and find that these modes correspond to the longitudinal acoustic (LA) or longitudinal optical (LO) branch along 24466

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The Journal of Physical Chemistry C the ΓM path in graphene (Figure S5, Supporting Information). The vibrational modes in Figure 4c also confirm the longitudinal vibration behavior. On the basis of this correspondence, we will further analyze the frequency
width behavior in Figure 4b. This low-energy mode actually has been discussed earlier and is named RBLM13 because it causes the ribbon width to reduce and expand like breathing, similar to the radial breathing mode in a nanotube. As shown in Figure 4c, RBLM has only one standing wave node (n = 1) in the middle, and thus we obtain its wave vector by using a formula q(m,n) = (n)/(m + 0.4)|ΓM| .18 Furthermore, the LA branch is approximately linear at low wave vector (i.e., ω = qv), where v is acoustic velocity. So eventually we have the formula ω = (ν)/ (m + 0.4)|ΓM| for RBLM. This relationship is more reasonable than an earlier one,13 which is linearly fitted to the classic Hooke’s law and gives a negative frequency at a large ribbon width. Finally, we would like to address the experimental detection issue. Since our present theory is within the context of the nonresonant scheme, the Raman intensity cannot be used to compare with the RRS data directly. Nevertheless, the SERS and TERS are appealing techniques to employ because they can greatly (up to 1014
1015 times for SERS31 and ∼104 times for TERS32) and almost equally enhance the Raman signals of all frequencies by inducing a very strong plasmon electric field around the metallic particles or tip, ensuring a direct comparison with our nonresonant Raman spectra. One advantage of SERS and TERS over RRS is that they can reflect vibrational properties of the entire sample rather than some of its components. Additionally, TERS possesses high spatial resolution and can be used to detect the signals at different positions, like the GNR edges. SERS and TERS have indeed been successfully applied in the study of graphene11,12 and carbon nanotubes,33 and therefore, we anticipate our results presented here to be verified by the SERS and/or TERS experiments in the future.

’ CONCLUSIONS On the basis of the DFPT, we have studied the nonresonant Raman spectra of the edge-hydrogenated AGNRs and ZGNRs. We find that the Raman spectra in both GNR types show a strong antenna effect, owing to the geometrical confinement effect in the out-of-plane and ribbon width directions. In AGNRs, the Raman spectra, especially the intensities, oscillate strongly with the ribbon width, while in ZGNRs, the Raman intensities first increase and then decrease with the ribbon width and the frequency
width relationship is closely related to the phonon dispersion of graphene along the ΓM direction. We explain this sharp difference between the two GNR types in terms of their different band structure variations with the ribbon width. Compared with the IR spectra of GNRs,18 we find that the Raman intensity is much more sensitive to the polarization, chemical bond type, and ribbon width. Compared with the earlier empirical Raman spectrum calculations,13,15 we reveal that the bondpolarization model is inadequate to describe the polarization feature, the width dependence behavior, and the Raman intensity accurately. We expect our calculations to be useful in clarifying the nonresonant Raman spectral behavior on the theoretical side and distinguishing the GNR types on the experimental side. ’ ASSOCIATED CONTENT

bS

Supporting Information. Dielectric function changes with respect to a small atomic displacement by using the sum-over-states

ARTICLE

approach; band gaps of the AGNRs; band gap versus Raman intensity for the E2g-like mode in the AGNRs; dielectric function of graphene and the ZGNRs; Raman intensity and frequency variation with ribbon width for peaks α, β, γ, and δ; phonon dispersion of the major Raman peaks in the ZGNRs and that of graphene along the ΓM direction. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] and [email protected].

’ ACKNOWLEDGMENT This work was partially supported by the NSFC (Grant Nos. 10774003, 10474123, 10434010, 90626223, and 20731162012), National 973 Projects (No. 2007CB936200, MOST of China), Program for New Century Excellent Talents in University of MOE of China, National Foundation for Fostering Talents of Basic Science (No. J0630311), Nebraska Research Initiative (No. 4132050400) of USA, and Grant-in-Aid for Next Generation Super Computing Project (Nanoscience Program), and Specially Promoted Research from the MEXT in Japan. Computational resources were provided by the University of Nebraska Holland Computing Center with the associated USCMS Tier-2 site at the University of Nebraska—Lincoln. G.L. acknowledges also the financial support from the China Scholarship Council. ’ REFERENCES (1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183–191. (2) Neto, A. H. C.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109–162. (3) Rao, C. N. R.; Sood, A. K.; Voggu, R.; Subrahmanyam, K. S. J. Phys. Chem. Lett. 2010, 1, 572–580. (4) Allen, M. J.; Tung, V. C.; Kaner, R. B. Chem. Rev. 2010, 110, 132–145. (5) Casiraghi, C.; Hartschuh, A.; Qian, H.; Piscanec, S.; Georgi, C.; Fasoli, A.; Novoselov, K. S.; Basko, D. M.; Ferrari, A. C. Nano Lett. 2009, 9, 1433–1441. (6) You, Y. M.; Ni, Z. H.; Yu, T.; Shen, Z. X. Appl. Phys. Lett. 2008, 93, 163112–163114. (7) Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; et al. Phys. Rev. Lett. 2006, 97, 187401–187404. (8) Calizo, I.; Bejenari, I.; Rahman, M.; Liu, G.; Balandinc, A. A. J. Appl. Phys. 2009, 106, 043509–043513. (9) Yoon, D.; Moon, H.; Son, Y. W.; Samsonidze, G.; Park, B. H.; Kim, J. B.; Lee, Y.; Cheong, H. Nano Lett. 2008, 8, 4270–4274. (10) Cancado, L. G.; Pimenta, M. A.; Neves, B. R. A.; MedeirosRibeiro, G.; Enoki, T.; Kobayashi, Y.; Takai, K.; Fukui, K.; Dresselhaus, M. S.; Saito, R.; et al. Phys. Rev. Lett. 2004, 93, 047403–047406. (11) Schedin, F.; Lidorikis, E.; Lombardo, A.; Kravets, V. G.; Geim, A. K.; Grigorenko, A. N.; Novoselov, K. S.; Ferrari, A. C. ACS Nano 2010, 4, 5617–5626. (12) Saito, Y.; Verma, P.; Masui, K.; Inouye, Y.; Kawata, S. J. Raman Spectrosc. 2009, 40, 1434–1440. (13) Zhou, J.; Dong, J. Appl. Phys. Lett. 2007, 91, 173108–173110. (14) Malola, S.; Hakkinen, H.; Koskinen, P. Eur. Phys. J. D 2009, 52, 71–74. (15) Saito, R.; Furukawa, M.; Dresselhaus, G.; Dresselhaus, M. S. J. Phys.: Condens. Matter 2010, 22, 334203–334208. (16) Guha, S.; Menendez, J.; Page, J. B.; Adams, G. B. Phys. Rev. B 1996, 53, 13106–13114. 24467

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