Discovering the forbidden Raman modes at the edges of layered materials.

The edges of layered materials have unique properties that substantially differ from the body regions. In this work, we perform a systematic Raman study of the edges of various layered materials (MoS2, WS2, WSe2, PtS2, and black phosphorus). The Raman spectra of the edges feature newly observed forbidden Raman modes, which are originally undetectable from the body region. By selecting the edge type and the polarization directions of the incident and scattered light, all forbidden Raman modes are distinctly detected. Optical simulations show that the edges of layered materials drastically distort the electromagnetic fields of both the incident and scattered light, so that the light interacts with the edges in a distinct way, which differs from its interactions with the body regions.

INTRODUCTION

Through the interaction between light and matter, Raman spectroscopy provides abundant materials information, including light-electron-phonon interactions, interatomic coupling, strain, defects, doping, carrier mobility, thermal conductivity, chemical components, and chemical functionalization (–). Recently, a rich library of layered materials has drawn intense interest due to their unusual physical properties (–). Raman spectroscopy has been widely used to investigate layered materials (–). However, certain Raman-active modes of layered materials are undetectable with the commonly used Raman backscattering configuration. For example, 2H-phase group 6 transition metal dichalcogenides (TMDCs; such as MoS2, WS2, and WSe2) have three Raman-active modes (, , and ) in the high frequency range. In previous studies, the and modes have been well detected, while the mode is a forbidden Raman mode (, ). The mode is undetectable, unless a broken symmetry is introduced (–). Similarly, black phosphorus (BP) has six Raman-active modes, which are , , , , , and . Among these modes, only , , and are experimentally detectable. These three vibrational modes contain information about in-plane anisotropy, and they have been used to identify the lattice direction of BP (). However, the other three Raman-active modes, , , and are forbidden and undetectable. These forbidden Raman modes have therefore been neglected in most previous studies and consequently bringing about incompleteness for the Raman spectroscopy of layered materials.

In addition, the terminal edges of layered materials exhibit unique magnetic, electronic, catalytic, topological, and optical properties that are in sharp contrast to those of the body region of the layered materials (–). However, there have been very few systematic Raman studies of the edges of layered materials (, ). In a recent study, two forbidden Raman modes of BP, and , were observed at the edges, and they were attributed to the presence of edge phonons (). However, the mechanism underlying the Raman process in the edge region needs to be verified by additional detailed experimental observations and analyses.

Here, we report on a systematic Raman study of the edges of various layered materials, including the 2H-phase MoS2, WS2, and WSe2, the 1T-phase PtS2, and BP. These experimental results demonstrate that all the forbidden Raman modes of layered materials (the mode of MoS2, WS2, and WSe2 and the , , and modes of BP) can be selectively detected at the edges. We find that the selective detection of these forbidden modes depends upon the edge type, the polarization direction of the incident light, and the polarization direction of the scattered Raman signal. By combining analysis of the experimental results with simulations, we have constructed a comprehensive model that attributes the appearance of these forbidden Raman modes to the distortion of electromagnetic field in the edge region. Because of their unique refractive properties, the edges of layered materials drastically change the polarization and propagation direction of light, which enables the forbidden Raman modes to be detected. The principle underlying this work can be extended to other layered materials, and we expect it to contribute to a more comprehensive understanding of the optical properties of the edge regions of layered materials.

RESULTS

Raman spectra from the edge region of 2H-phase TMDCs

In this study, we investigated a variety of layered materials, including the 2H-phase MoS2, WS2, and WSe2, the 1T-phase PtS2, and BP. We mechanically exfoliated the layered material flakes from the bulk crystals onto a Si/SiO2 substrate. We then collected microscopic Raman spectra from the exfoliated flakes using the common backscattering configuration, as shown schematically in Fig. 1A. First, we focus on the Raman modes of the 2H-phase MoS2. Figure 1B shows a schematic diagram of the three Raman-active modes of 2H MoS2: , , and . The signal intensities of the three Raman modes are shown in table S1. They are given by the Raman scattering formula I = ||2, where is the Raman tensor, is the polarization direction of the incident light, and is the polarization direction of the scattered Raman signal. The mode is a forbidden Raman mode because its intensity is strictly zero. A more detailed discussion of the Raman mode is presented in section S2. The Raman spectra of MoS2 from the body region and the edge region are collected and compared in Fig. 1C. The body region exhibits only the and modes at 385 and 410 cm−1. In sharp contrast, a new peak emerges in the Raman spectrum from the edge region. The position of the new peak exactly corresponds to the forbidden mode at 287 cm−1. Although the intensity of the mode is less than 20% of the normal and modes, it is much higher than the noise level and is sufficiently distinct for further studies.

Fig. 1

Raman spectroscopy of MoS2.

(A) Schematic illustration of Raman backscattering spectroscopy. (B) Raman-active modes of 2H-phase TMDCs in the high frequency range. (C) Raman spectra of MoS2 from the edge and from the body region. a.u., arbitrary units. (D) Optical image of a specific MoS2 flake with the orthogonal armchair and zigzag edges. The intensity of signal is shown in (E) for [, ] = [X, X], (F) for [, ] = [Y, Y], (G) for [, ] = [X, Y], and (H) for [, ] = [Y, X]. The white arrows in (E) to (H) indicate the positions of the edges, corresponding to the black one-way arrows in (D).

To obtain a fundamental understanding of the appearance of the mode, we further study its dependence on the edge type (zigzag or armchair), the polarization direction of the incident light (), and that of the scattered Raman signal (). Figure 1D shows the optical image of a specific MoS2 flake with the orthogonal armchair and zigzag edges. The crystal orientation and the edge type of MoS2 can be identified by a method reported in the recent literature (). We designate the direction of the armchair edge as X and the direction of the zigzag edge as Y. The polarization directions of the incident light and the scattered Raman signal ( and ) are set along X or Y, respectively. By mapping the intensity of the mode, we find that for the armchair edge (X), the mode appears when [, ] = [Y, Y] (Fig. 1F), [X, Y] (Fig. 1G), or [Y, X] (Fig. 1H), but it disappears when [, ] = [X, X] (Fig. 1E). For the zigzag edge (Y), the mode appears when [, ] = [X, X] (Fig. 1E), [X, Y] (Fig. 1G), or [Y, X] (Fig. 1H), but it disappears when [, ] = [Y, Y] (Fig. 1F). Intensity maps of the and modes are shown in fig. S2. Detailed Raman spectra from the body region, the armchair edge, and the zigzag edge are shown in fig. S3, with [, ] = [X, X], [Y, Y], [X, Y], and [Y, X]. Note that the peak position of the mode remains at 287 cm−1 for all the Raman spectra, with no red or blue shift, regardless of the edge type or the polarization directions and .

In a similar way, we studied the Raman spectra of the 2H-phase WS2 and WSe2, which have atomic structures and Raman modes identical to those of MoS2. As shown in Fig. 2, we collected and compared the Raman spectra for WS2 (Fig. 2, A to C) and WSe2 (Fig. 2, D to F) from the body region, the armchair edge, and the zigzag edge. In Fig. 2A, the body region of WS2 exhibits only the and modes at 356 and 421 cm−1. Figure 2 (B and C) presents the Raman spectra of WS2 from the armchair and zigzag edge regions. In contrast to the body region, the forbidden mode at 297 cm−1 appears at the armchair edges when [, ] = [X, Y], [Y, X], or [Y, Y] (Fig. 2B) and at the zigzag edges when [, ] = [X, X], [X, Y], or [Y, X] (Fig. 2C). For WSe2, the Raman peak positions of and are 248 and 252 cm−1, which are very close to each other. The intensity of the mode is much larger than that of the mode. As shown in Fig. 2D, the body region of WSe2 shows only one merged peak when [, ] = [X, X] or [Y, Y], which is dominated by the mode. When [, ] = [X, Y] or [Y, X], the peak vanishes, and the peak emerges. Figure 2 (E and F) presents the Raman spectra of WSe2 from the armchair and zigzag edge regions, respectively. The forbidden mode at 176 cm−1 appears at the armchair edges when [, ] = [Y, Y], [X, Y], or [Y, X] (Fig. 2E) and at the zigzag edges when [, ] = [X, X], [X, Y], or [Y, X] (Fig. 2F). Therefore, for MoS2, WS2, and WSe2, the forbidden mode is detectable selectively at the edge regions, and the appearance of the peak depends on the edge type and the directions of and in the same way.

Fig. 2

Raman spectra of WS2 and WSe2.

(A to C) Raman spectra of WS2 from (A) the body region, (B) the armchair edge, and (C) the zigzag edge. (D to F) Raman spectra of WSe2 from (D) the body region, (E) the armchair edge, and (F) the zigzag edge. The spectra vary with the polarization direction of the incident light and the scattered Raman signal (X or Y).

So far, we have obtained the forbidden peaks of MoS2, WS2, and WSe2 from the edges. We find that the peak positions of the forbidden modes of 2H-phase TMDCs (Fig. 3) are correlated with those of the modes, as indicated by Eq. 1where Δ and Δ are the shifts in the peak positions of the and modes, and mchal and mmetal are the atomic masses of the chalcogenide and the metal in the TMDCs, respectively. We obtained the Raman shifts of 2H-phase MoTe2 and MoSe2 from the literature (, ). The fitting coefficient α is 0.966. The principle underlying Eq. 1 involves atomic lattice vibration dynamics. As illustrated in the inset in Fig. 3, for the phonons, only the chalcogenide atoms are involved, vibrating in opposite directions, and the effective mass is M = 4mchal. For the phonons, all the chalcogenide atoms vibrate in opposition to the metal atoms, and the effective mass is M = 4mchal·mmetal/(2mchal + mmetal). The frequencies of the long-wavelength optical modes are given bywhere ω and ω are the eigenfrequencies of the phonons, which are proportional to the Raman shifts. The quantities β and β are elastic constants, which are related to the interatomic interactions. With ω: ω = Δ: Δ, and inserting Eq. 2 into Eq. 1, we obtain β: β = α2 = 0.932. This result indicates that the relative vibration direction of the Janus chalcogenide atoms in the 2H-phase TMDCs makes a subtle difference to the interatomic interaction, whether in the opposite ( mode) or the same ( mode) direction.

Fig. 3

Raman shift ratio of the E1g and E2g as a function of the atomic mass ratio in 2H-phase TMDCs.

Raman spectra from the edge region of BP

In addition to the forbidden Raman modes of MoS2, WS2, and WSe2, we also investigated the Raman modes from the edge regions of BP. Figure 4A shows a BP flake with its orthogonal armchair and zigzag edges. As above, we denote the direction of the armchair edge as X and the direction of the zigzag edge as Y. The Raman-active modes of BP in the high frequency range are schematically illustrated in Fig. 4B. The intensities of the active modes of BP are calculated according to table S1. Among the six Raman-active modes, , , and are detectable, while , and are forbidden. Figure 4C shows the Raman spectra from the body region of BP. The , , and are present at 362, 439, and 467 cm−1, respectively, and their intensities vary as functions of and . We further collect the Raman spectra from the armchair edge of BP (Fig. 4D) and from the zigzag edge (Fig. 4E). The three forbidden Raman modes, , and , appear in the edge regions. The peak, located at 195 cm−1, appears at the armchair edge when [, ] = [Y, Y] (Fig. 4D) and at the zigzag edge when [, ] = [X, X], [X, Y], or [Y, X] (Fig. 4E). The peak, located at 230 cm−1, appears at the armchair edge when [, ] = [X, Y] or [Y, X] (Fig. 4D) and at the zigzag edges when [, ] = [X, X] (Fig. 4E). The peak position of the mode is 436 cm−1, which is very close to the mode at 439 cm−1. Thus, the peak of mode is submerged by the intense peak of mode when [, ] = [X, Y] or [Y, X]. The mode appears at the zigzag edge when [, ] = [X, X] (Fig. 4E), when the mode has almost vanished. Therefore, all the three forbidden Raman modes of BP are detected from the edge regions, depending upon the edge type and the directions of and .

Fig. 4

Raman spectroscopy of BP.

(A) Atomic structure and image of a BP flake with the orthogonal armchair edge and the zigzag edge. (B) Raman-active modes of BP in the high frequency range. (C to E) Raman spectra of BP from (C) the body region, (D) the armchair edge, and (E) the zigzag edge. The spectra vary with the polarization directions (X or Y) of the incident light and the scattered Raman signal .

Raman spectra of 1T-phase PtS2

Last, we studied the Raman spectroscopy of 1T-phase PtS2. PtS2 has only two Raman-active modes in the high frequency range, which are and (). Both modes are normal and unforbidden, with the commonly used backscattering configuration, as shown in table S1. Raman spectroscopy from the edges of PtS2 is identical to that from the body region. No new peaks besides the and modes emerge at the PtS2 edges, as shown in fig. S4.

Theoretical modeling

We have demonstrated that the forbidden Raman modes of various layered materials, which are usually undetectable and have been neglected in previous work, can be selectively detected from the edge regions. A recent study has reported observations of the and modes from the BP edges. They attributed these forbidden modes to the presence of edge phonons (). However, some experimental observations cannot be explained by this theory: (i) The frequency of edge phonon is sensitive to the atomic structures, while the new peaks at the zigzag edge and the armchair edge have the same peak positions. (ii) Edge phonons have a broad full width at half maximum (FWHM) because the reconstructed structure is close to an amorphous phase. However, the FWHM of the new peaks is as small as that of normal Raman peaks (a few cm−1) from the crystalline body region. (iii) Edge phonons include multiple modes, while the new peaks correspond only to the forbidden Raman modes. A more detailed analysis is included in section S6. In the following discussion, we construct a model to explain the mechanism and provide an alternative explanation for the appearance of these forbidden Raman modes. We focus on how the edges of layered materials distort the electromagnetic fields of both the incident light and the scattered Raman light, and we then derive a revised Raman intensity formula for the selective appearance of forbidden Raman modes at the edge region of layered materials.

Using the finite element method, we first simulate the incident light at the MoS2 edge region. Figure 5 (A and B) shows the simulated electric field amplitudes and their components in the x, y, and z directions at the edge region, where the cross-profile is oriented along the xz plane and the edge direction is in the y direction. As a typical layered material, MoS2 has anisotropic dielectric constants (or birefringent refractive indices). The in-plane and out-of-plane relative dielectric constants are ε = 20 + 15i and ε = 4 + 0.3i, respectively (–). In Fig. 5A, the incident light from the z direction is polarized in x, with i = (1, 0, 0). The incident light is polarized perpendicular to the edge (y). Inside the MoS2 edge region, the y-polarized component |E| remains zero. The z-polarized component |E| originates from the edge region to satisfy the continuity boundary conditions for Maxwell’s equations. Note that |E| dominates the electric field in the edge region, rather than the original field |E|. The amplitude of |E| is larger than that of |E| because of the strong dielectric anisotropy of MoS2. The real and imaginary parts of ε are, respectively, 5 and 50 times larger than those of ε, indicating that the electric field in the x direction is mostly screened by polarization charges and damps quickly inside MoS2. Therefore, the actual polarization direction of the incident light inside the edge region becomes iedge = (δi, 0, δi), instead of the original i = (1, 0, 0). By similar reasoning, for the cases in which the polarization direction of the incident light is orthogonal to the edge direction, i.e., (edge type = X, i = Y) or (edge type = Y, i = X), a z-polarized component |E| arises, and a non-negligible δ must be included. In Fig. 5B, we further simulated the cases for which the polarization direction of the incident light is parallel to the edge direction. The incident light is set polarized in y. In contrast to the results shown in Fig. 5A, the polarization direction in this case remains unchanged inside the MoS2. The components |E| and |E| remain zero, and the actual iedge remains (0, 1, 0). Therefore, in cases that the polarization direction of the incident light is parallel to the edge direction, i.e., (edge type = X, i = X) or (edge type = Y, i = Y), the electric field component of the incident light remains unchanged.

Fig. 5

Electric field of the incident light and the scattered Raman signal at the edge of a MoS2 flake.

The cross-profile is in the xz plane, with the edge direction along y. (A) The incident light from the z direction is polarized in the x direction with i = (1, 0, 0). (B) The incident light from the z direction is polarized in y direction with i = (0, 1, 0). The electric field amplitude is shown in (A) and (B). (C) Scattered Raman light with original polarization along z, a portion of the light propagates in the z direction with its polarization direction in x.

The presence of the edges distorts not only the incident light but also the scattered Raman light. In section S2, we have simulated the scattering of the signal from the body region of MoS2. The incident light polarized in the xy plane generates signal polarized in the z direction. The z-polarized signal propagates along the xy plane and is soon reabsorbed by the MoS2 itself. Thus, the signal cannot be collected and detected (see fig. S1). However, when the scattered signal meets a terminal edge, the direction of propagation is markedly changed. As shown in Fig. 5C, at the edge region, the electromagnetic field of the 1g signal is distorted, and its propagation direction diverges at the edge. A portion of the 1g signal propagates in the z direction with its polarization direction in x. Thus, the 1g mode signal is detectable from the z direction, and the effective polarization direction sedge becomes (δs, 0, δs), rather than the original s = (1, 0, 0). Therefore, the edge changes the propagation direction of the Raman signal while keeping the polarization direction perpendicular to the edge. In the cases that (edge type = X, s = Y) and (edge type = Y, s = X), a non-negligible δ must be included. While in the cases that the polarization direction of the scattered light is parallel to the edge direction, i.e., (edge type = X, s = X) or (edge type = Y, s = Y), the s remains unchanged.

From the above simulations, we see that the edges markedly distort the electromagnetic field of both the incident light and the scattered light. As a result, the intensities of the Raman modes, I = ||2, are modified to Iedge = |edge·edge|2. The detailed calculation is given in section S7, and the updated expressions for Iedge of the forbidden Raman modes from the edges are listed in Table 1. We also develop the method to quantitatively compute Iedge, as shown in section S8. Similar analyses are applicable to the other layered materials studied in this work, including WS2, WSe2, and BP. Our theoretical model matches the experimental observations well. The forbidden Raman modes with nonzero Iedge are experimentally detected, depending upon the edge type and the polarization directions of incident and scattered light. A minor exception is the very weak peak observed at a zigzag edge (Y) with [, ] = [X, X]. This may be due to the imaginary parts of the Raman tensor and the birefringence of BP, which have been reported to produce abnormal Raman responses (, ).

Table 1

Calculated expression of Iedge for the forbidden Raman modes.

Correspondingly, a “yes” indicates that the mode is experimentally detected, while a “no” indicates that the mode is not experimentally detected. N/A, not applicable.

E1g mode of MoS2,WS2, and WSe2		[ei, es]
		[X, X]	[Y, Y]	[X, Y]	[Y, X]
Armchair (X)	Iedge	0	d2 (δiz2δsy2 + δiy2δsz2)	d2δsz2	d2δiz2
	Detected	No	Yes	Yes	Yes
Zigzag (Y)	Iedge	d2 (δiz2δsx2 + δix2δsz2)	0	d2δiz2	d2δsz2
	Detected	Yes	No	Yes	Yes
B1g of BP		[ei, es]
		[X, X]	[Y, Y]	[X, Y]	[Y, X]
Armchair (X)	Iedge	0	h2 (δiz2δsy2 + δiy2δsz2)	0	0
	Detected	No	Yes	No	No
Zigzag (Y)	Iedge	0	0	h2δiz2	h2δsz2
	Detected	Yes (weak)	No	Yes	Yes
B13g of BP		[ei, es]
		[X, X]	[Y, Y]	[X, Y]	[Y, X]
Armchair (X)	Iedge	0	0	i2δsz2	i2δiz2
	Detected	No	0	Yes	Yes
Zigzag (Y)	Iedge	i2 (δiz2δsx2 + δix2δsz2)	0	0	0
	Detected	Yes	No	No	No
B23g of BP		[ei, es]
		[X, X]	[Y, Y]	[X, Y]	[Y, X]
Armchair (X)	Iedge	0	0	j2δsz2	j2δiz2
	Detected	No	No	N/A	N/A
Zigzag (Y)	Iedge	j2 (δiz2δsx2 + δix2δsz2)	0	0	0
	Detected	Yes	No	N/A	N/A

Similar analysis should also be applicable to other types of edge sites, such as the grain boundaries of polycrystalline layered materials, where the refractive index may also change across the edge sites, as described in detail in section S9. We also recognize the forbidden Raman modes detected from the powder and dispersion samples (fig. S9), which possibly relate to the edge sites to a certain degree. In addition to Raman scattering, the principle of this model is also applicable to other light-matter interactions, such as photoluminescence, Rayleigh scattering, and high-order harmonic generations.

DISCUSSION

In summary, we have demonstrated that all the forbidden Raman modes of layered materials ( of 2H-phase MoS2, WS2, and WSe2 and , , and of BP) are detectable from the edges. The selective detection of these forbidden Raman modes depends upon the edge types and the polarization directions of the incident light and scattered Raman signals. We have constructed a comprehensive model to clarify the underlying mechanism, which is related to the markedly distorted electromagnetic fields at the layered material/air interfaces. We expect this work to provide a method for probing the forbidden Raman modes of layered materials, contribute to a more complete comprehension of Raman spectroscopy, and inspire a more detailed research on the unique optical properties of the edge regions of layer materials.

MATERIALS AND METHODS

Material preparation

MoS2, WS2, WSe2, PtS2, and BP flakes were obtained by exfoliating the bulk samples onto 300-nm SiO2/Si substrates. The thickness of the flakes was measured by the atomic force microscope (MoS2, 56 nm; WS2, 47 nm; WSe2, 148 nm; PtS2, 248 nm; BP, 106 nm). For layered material flakes thinner than 30 nm, we were not able to experimentally detect the forbidden Raman modes.

Raman characterization

Raman spectroscopy was conducted using a 488-nm laser as the incident light, with a spot size of ~1.5 μm. We tuned the polarization direction of the incident light with a half-wave plate. We collected the scattered Raman light with a 50× lens with a numerical aperture of 0.55, and we selected the polarization direction with a polarizer plate. We performed two-dimensional mapping with a step size of 0.5 μm.