Observation of forbidden phonons and dark excitons by resonance Raman scattering in few-layer WS$_2$

TL;DR

This study uses resonance Raman scattering to explore exciton-phonon interactions in few-layer WS₂, revealing forbidden phonons, dark excitons, and quantum interference effects, advancing understanding of 2D material optoelectronics.

Contribution

It demonstrates the detection of forbidden phonons and dark excitons via resonance Raman scattering in 2D WS₂, providing new insights into exciton-phonon coupling and many-body effects.

Findings

Detected forbidden phonons unobservable in ordinary Raman.

Resolved bright and dark exciton state structures.

Observed quantum interference between phonons and excitons.

Abstract

The optical properties of the two-dimensional (2D) crystals are dominated by tightly bound electron-hole pairs (excitons) and lattice vibration modes (phonons). The exciton-phonon interaction is fundamentally important to understand the optical properties of 2D materials and thus help develop emerging 2D crystal based optoelectronic devices. Here, we presented the excitonic resonant Raman scattering (RRS) spectra of few-layer WS$_2$ excited by 11 lasers lines covered all of A, B and C exciton transition energies at different sample temperatures from 4 to 300 K. As a result, we are not only able to probe the forbidden phonon modes unobserved in ordinary Raman scattering, but also can determine the bright and dark state fine structures of 1s A exciton. In particular, we also observed the quantum interference between low-energy discrete phonon and exciton continuum under resonant excitation. Our works pave a way to understand the exciton-phonon coupling and many-body effects in 2D materials.

Equations

$$I=I_0\frac{(1+(\omega -{\omega }_0)/q\gamma {)}^2}{1+((\omega -{\omega }_0)/\gamma {)}^2}$$

$$\begin{array}{rl}& P\propto \mid \frac{⟨i|H_{eR}({\omega }_s)|m^{\prime }⟩⟨m^{\prime }|H_{eL}|m⟩⟨m|H_{eR}({\omega }_i)|i⟩}{(E_{m^{\prime }}-\hslash {\omega }_i-i{\gamma }_{m^{\prime }})(E_m-\hslash {\omega }_s-i{\gamma }_m)}\\ & +\frac{⟨i|H_{eR}({\omega }_i)|m⟩⟨m|H_{eL}|m^{\prime }⟩⟨m^{\prime }|H_{eR}({\omega }_s)|i⟩}{(E_m-\hslash {\omega }_i-i{\gamma }_m)(E_{m^{\prime }}-\hslash {\omega }_s-i{\gamma }_{m^{\prime }})}{\mid }^2\end{array}$$

Full text

The exciton-phonon interaction plays an important role in determination of optical properties in semiconductors and related optoelectronic devices performances. For instance, strong exciton-phonon coupling can strongly enhance the phonon-assisted anti-Stokes luminescence upconversion and leads to net optical refrigeration of semiconductorsZJ-Nature-2013 . Particularly, when the exciton-phonon coupling is only efficient between specific phonon branch and exciton state, many interesting optical phenomena are emerged such as resolved sideband Raman cooling of optical phonons in semiconductorsZJ-NP-2016 , phonon-exciton polaritonpolaritons-prb-1979 , and multi-phonon replica of exciton hot-luminescenceCdS-PRL . In those experiments, resonant Raman scattering (RRS) was extensively used to detect and study the exciton-phonon interaction.

Two dimensional (2D) Layered transition metal dichalcogenides (TMDs) with stoichiometry of MX2 (M=Mo, W; X=S, Se, Te) offer a platform with both strong exciton-photon and exciton-phonon interaction effectsPhysRevB-85115317-2012 ; Carvalho-prl-2015 . In few-layer MX2, owing to the dielectric screening and spatial quantum confinement in 2D systems, their optical transitions and light-matter interaction are governed by robust exciton feature with binding energies of several hundred meV um-nm-2014 ; Qiu-PRL-2013 ; cuixiaodong-serp-2015 . Due to strong spin-orbit (SO) coupling and exciton-phonon interaction, it allows to study the spin-valley circular dichroismXu-NPRiew-2016 ; Cao-NC-2012 ; cuixiaodong-PNAS-2014 ; cuixiaodong-review-2015 , dark excitonDark-exciton-nature-2014 , phonon-assisted excitonic luminescence upconversion NP-xuxiaodong-2016 , valley selective exciton-phonon scatteringmm-arXiv-2017 , and dipole-type polaritonic excitations NM-LowT-2017 .

Raman scattering is a powerful tool to detect the phonon dynamics 2D materialsZhang-Xin-CSR-2015 ; Lux-nanoresarch-2016 . In particular, Raman spectroscopy can be used to detect the interlayer coupling and exactly determine the layer number of 2D sample Tan-nm-2012 ; Zhao-nanoletter-2013 . When the laser energy is close to the exciton transitions of TMDs, RRS allows people to explore the exciton-phonon couplingSun-PRL-2013 ; del-corro-nanolett-2014 ; MAA-PRB-2014 ; mote2-prb-2016 ; MoSe2-prb-2016 ; Wu-nc-2014 , symmetry-dependent properties of exciton-phonon scattering Carvalho-prl-2015 ; del-nanolett-2016 , phonon assisted intervalley scattering CBR-Naturecom-2017 ; PhysRevLett-117-2016 ; WSe2-prl-2015 , etc. Up to now, most of RRS experiments in MX2 only focus on high frequencies Raman modes of MX2, while the ultra-low frequency phonon RRS (below 50 cm*-1*) has rarely been reported. Since ultra-low frequency phonon modes have a very small energy of several meV, we can use it to explore the fine-structure of excitonic energy sates such as small splitting excitonic levels. Secondly, some forbidden phonon modes and excitonic states become observable and active in RRS experiments based on parity selection rulecu2o-prb-1973 ; cu2o-prl-1973 : in ordinary non resonance Raman scattering, only Raman active phonons with even parity can be observed but infrared (IR) active phonons with odd parity cannot be observed; however, in RRS situation, the odd-parity IR-active phonons can be activated when the Raman transition includes the electronic-dipole forbidden excitons with even parity (dark excitons). Since the dark and bright excitons governs the optical properties of 2D TMDsDark-exciton-nature-2014 and affects the performances of 2D based opto-electronic devicesYeyu-Natphoton-2015 , it is thus crucial to detect the bright-dark exciton fine-structures and determine their splitting energy in TMDs. Recently there are several experimental techniques such as two-photon absorption/photoluminescence and temperature dependent time-resolved photoluminescence have been used to probe the dark excitons in TMDs Dark-exciton-nature-2014 ; trion-NC-2016 ; ZhangXX-prl-2015 . However, those methods can’t detect the forbidden-phonon and dark excitons simultaneously and thus can’t provide detail information of the exciton-phonon coupling related to forbidden phonons and dark excitons.

Furthermore, when the discrete phonon mode couples with a continuum state such as electron occupation states, the phonon lineshape became an asymmetry Breit-Wigner-Fano (BWF) resonance lineshape (in short Fano resonance), which is fundamental important in the interpretation of light propagation, optical spectra and electronic transport in semiconductorsFano-pr-1961 ; RevModPhys-fano-review ; FANORESONANCE-NM-2010 . The Fano resonance of phonon Raman spectra has been widely studied in doped siliconsemifano-prb-1975 , graphitic materialsnanotube-nature-1997 ; PhysRevLett-graphene-2009 ; Tan-nm-2012 , and layered topological insulatorZJ-nanolett-2011 , charge density wave and superconductor statesRevModPhys-fano-review ; RevModPhys-79-75 , etc. However, to the best of our knowledge, there are few reports about the exciton-phonon Fano resonance in MX2.

Here, we investigated forbidden phonons, dark excitons and exciton-phonon interactions in few-layer WS2 by using of RRS techniques up to 11 excitation laser lines to finely resonate with A, B and C exciton transition from 4 to 300 K.

Results

Like other MX2 TMDs, WS2 shares the same hexagonal crystalline structure. Each layer is composed of three atomic layers, one W layer sandwiched between two S layers, and we therefore refer them as a trilayer (TL). The W and S atoms could occupy different trigonal sites, forming different polytypes. For Mo and W dichalcogenides, 2H (here H stands for hexagonal) is the most stable and common polytype in nature, where two adjacent atomic layers keep alternating at A and B sites.

Figure 1(a) shows the reflectance contrast spectra $\Delta{R}/R$ for 1TL, 2TL, and 3TL WS2 on SiO2 substrate at room temperature. Two features around 1.98 and 2.35 eV, denoted by A and B exciton, is attributed to the interband dipole-allowed exciton transitions between the spin-orbit split valence band and the lowest conduction at K (or K’) point of the Brillouin zone, respectivelyMark-F-prl-2010 ; LYL-PRB-2014 . The broad peak around 2.7 eV, denoted by C exciton, is from transition between the highest valence band and the first three lowest conduction bands around the $\Gamma$ point of the Brillouin zoneQiu-PRL-2013 . While the features N and D peaks around 2.15 and 3.0 eV are not clear so far. Both the energies of A and B exciton in 1TL are slightly larger than that in 2TL and 3TL WS2. In contrast to A and B exciton transitions, the energy of C exciton transitions red shifts to 2.7 eV in 3TL from around 2.8 eV in 1TL.

Since the energy of each exciton in WS2 is distinct from each other, it provides a perfect platform to study the excitonic RRS behavior in WS2. Figure 1(b) and 1(c) shows the ultra-low frequency RRS spectra excited by 11 laser lines on 2TL and 3TL WS2, respectively. When the excitation energies ($\varepsilon_{ex}$) are resonant with C exciton transitions in the range of 2.81 to 2.54 eV, we only observed the interlayer shear modes (SMs) and interlayer breathing modes (LBMs), of which frequencies are strictly depend on the layer numbersTan-nm-2012 ; Zhang-prb-2013 ; Zhao-nanoletter-2013 . We also measured the Raman spectra of 1-5TL, 7TL, and bulk WS2 excited by 2.71 eV laser as shown in supporting Figure S1(a). There are no new modes below 50 cm*-1* been found expect SMs and LBMs, of which frequencies match very well with theoretical results calculated by liner chain model (LCM)lixl-nt-2016 , as shown in supporting Figure S1(b). Here we define the SMN1 is the highest frequency branch and SMNN-1 is the lowest frequency branch of the SMs, where N refers to the layer numbers of sample and N-1 refers to the (N-1)th branch of SMsZhao-nanoletter-2013 ; Zhang-Xin-CSR-2015 . Similarly, the LBMN1 and LBMNN-1 are the highest and lowest frequency branch of the LBMs, respectively. Therefore, we can use those modes as a fingerprint to unambiguously identify the layer numbers of WS2.

When the $\varepsilon_{ex}$ is close to B exciton transitions (2.41 to 2.18 eV), besides the SM and LBM, we also observed two new peaks located at 27.8 and 45.4 cm*-1*, which frequencies are independent on the $\varepsilon_{ex}$ and layer numbers. In 2TL and 3TL, the peak at 45.4 cm*-1* is not so pronounced as 27.8 cm*-1* peak, but we can still resolve it. As being discussed in later part, we tentatively assign them as acoustic phonons with finite wavevector k and labeled them as TA and LA, respectively. While the excitation energy is around 2.09 eV, in the middle of A and B exciton transitions, these two wavelength-independent peaks almost vanished. When the $\varepsilon_{ex}$ is close to A exciton transitions (1.92 and 1.96 eV), we observed another new peak with asymmetric Fano lineshape. We noted that its frequency is close to SMNN-1. Therefore, we proposed that this Fano lineshape mode is from the interference between SMNN-1 phonons and continuum electronic states when $\varepsilon_{ex}$ is resonant with A exciton transition. We will give more evidences to certify this assignment in later part.

In Figure 1(d), we plotted the RRS profiles of three representative Raman modes of LBM21, TA and SM21 of 2TL WS2. Interestingly, these three kinds of phonon modes show different resonance profiles. The LBM21 shows a resonant enhancement at the A and C exciton transitions; the TA mode is enhanced at both of A and B exciton resonances. More interestingly, the SM21 shows a Fano lineshape when incident lasers are close to A exciton transition, while it became a Lorentzian lineshape when incident laser is off-resonant with A exciton. We also measured RRS spectra of other high frequency modes (See Figure S2 in supplementary information). As shown in supporting Figure S2(c), all of phonons contributed from high symmetry points in Brillouin zone, including 2LA(M), $E^{\prime}(M)-LA(M)$ and $A^{\prime}_{1}$(M)-LA(M)Zhang-Xin-CSR-2015 ; ShiW-2D-2016 , show incident resonant enhancement at A and B exciton transition. Differently, the A1g mode is incidentally resonant enhanced at A, B and C exciton transitions, while E${}_{2g}^{1}$ mode is only strongly enhanced at C exciton resonance. This distinct electron-phonon coupling can be explained by considering the symmetries of the phonons and of the exciton orbitals associated with the A, B, and C excitons Carvalho-prl-2015 .

In order to understand the physical origins and confirm assignments of new observed Raman peaks, we have conducted the RRS measurements at A and B exciton resonance for different layer numbers, polarization Raman configurations, and sample temperature, respectively. Figure 2(a) shows the ultra-low frequency RRS spectra of 1-5TL, 7TL, and bulk WS2 sample excited by 2.34 eV laser, which is close to B exciton transitions. Besides SMN1 and LBMNN-1 peaks, the 27.8 cm*-1* mode can be observed for all samples, while the mode at 45.4 cm*-1* is only absent in monolayer case may due to the too weak scattering cross-section. As shown in Figure 2(b), the 27.8 cm*-1* mode is polarization dependent, while the mode at 45.4 cm*-1* is depolarized. Figure 2(c) shows the frequencies of TA, LA, SMN1 and LBMNN-1 as a function of layer numbers of WS2. Obviously, the frequencies of SMN1 and LBMNN-1 are strictly depend on the layer numbers, while the frequencies of TA and LA are not only independent on the layer numbers, but the excitation energies, as shown in Figure 2(c) and Figure 1(b-c). We noted that the peak at 45.4 cm*-1* shows a clearly asymmetrical Fano-like lineshape, which became much more obvious in the case of cross (VH) polarization due to suppressive background signals. The peak at 45.4 cm*-1* is fitted by Fano function RevModPhys-fano-review ; ZJ-nanolett-2011 :

[TABLE]

where the ${\omega_{0}}$ is uncoupled phonon frequency, q is the asymmetry parameter, and $\gamma$ is the full-width-half-maxium (FWHM) of uncoupled phonon modes. In coupled resonance, the peak frequency of Fano lineshape becomes $\omega_{0}+\gamma/q$ and Fano FWHM becomes 2$\gamma|(q^{2}+1)/(q^{2}-1)|$. For positive q, the Fano peak frequency is blueshifted related to the uncoupled phonon, but it is redshifted for negative q. In Fano resonance, the peak linewidth is always broader than intrinsic phonon linewidth no matte positive or negative q when $|\emph{q}|>1$. The dimensionless parameter ${1/\emph{q}}$ characterizes electron-phonon coupling strength: a stronger coupling (q$\to$0) causes the peak to be more asymmetric. In the limit of weak electron-phonon interaction (q$\to\infty$), Fano lineshape is reduced to a Lorentzian lineshape. Such electron-phonon interaction caused BWF lineshape has been observed in 2D materials, such as grapheneZhangYB-NN-2010 ; Tan-nm-2012 and $Bi_{2}Se_{3}$ 2D crystalsZJ-nanolett-2011 . As shown the fitting curve in Figure 2(b), we got $1/q=-0.29$, which is almost a constant for different layer numbers. As shown in Figure 2(c), this negative value of q leads to the peak frequencies of LA Fano modes are redshifted related to uncoupled LA phonon, which the frequencies are obtained by Fano fitting. The $|1/\emph{q}|<1$ reflects the 45.4 cm*-1* phonon mode is dominant in Fano resonanceZhangYB-NN-2010 .

Based on the lineshape, linewidth and Stokes/anti-Stokes components, we proposed that these modes independent on layer number and excitation energies belong to the lattice phonon rather than other quasi particles such as electronic plasmon. The reason is that the electronic plasmon Raman scattering usually is observed in heave doped sample with very broad single Stokes peakAbstreiter1984 . Since these two modes are independent on the layer numbers, they may belong to acoustic phonons. As shown in Figure S3 in supplementary information, there are only acoustic phonons in 1TL bellow 60 cm*-1*; in few-layer sample, both of SMs and LBMs are layer number dependent. As results, only acoustic phonons with finite k can explain physical origin of these modes. Another evidence for this assignment is to compare the ratio of two mode frequencies and ratio of acoustic velocity related two acoustic phonon branches. We found that the ratio of longitudinal acoustic (LA) velocity (1080 $m/s$) to transvers acoustic (TA) velocity (668 $m/s$) Phonondispersion-2011 exactly matches the ratio of 45.4 cm*-1* to 27.8 cm*-1*. Additionally, by comparing the their polarization dependence with Raman tensors of LA and TA vibrationZhao-nanoletter-2013 , we also found that 45.4 cm*-1* mode has the same depolarized properties as LA Raman tensor, and TA phonon Raman tensor matches polarized properties of the 27.8 cm*-1* mode. Therefore, we assigned 27.8 and 45.4 cm*-1* modes as TA and LA phonons with finite k near the Brillouin center, respectively. Based on Figure S3, we can find the $\emph{k}\simeq 3\times$107 cm*-1*, which is very close to center of Brillouin zone but much larger than wavevector of incident light (k${}_{light}\simeq 10^{5}$ cm*-1*). In resonance condition, the phonons with finite k can be involved in the Raman scattering though elastically scattered by a zero energy defect states with -k. In this case, both of the momentum and energy are conversed. The similar phenomena have been observed in RRS spectra of graphene.Ferrari-200747 The detailed physical mechanism behind the emerging of these acoustic modes calls for further studies.

We also conducted the RRS experiments resonated with A exciton in 1-5TL, 7TL, and bulk WS2 excited by 1.96 eV and 1.92 eV as shown in Figure 3(a) and supporting Figure S4, respectively. In A exciton resonance case, the TA mode can still be clearly resolved at 27.8 cm*-1*, which has the same frequency as observed at B exciton resonance. However, LA mode is too weak to be resolved, as shown in Figure 3(a). Since the background signal can be efficiently suppressed under VH polarization configuration, we conducted the RRS measurements with the same excitation energy under the VH polarization as shown in Figure 3(b). In contrast to the VH RRS spectra measured at B and C exciton transitions as shown in Figure 2(b), all of SMNN-1 modes are disappeared, and SMN1 modes can be resolved with a very weak intensity in 5TL and 7TL WS2. The LA mode also shows much weaker intensity compared with spectra under the B exciton resonance condition, but it can still be resolved. The detailed reasons call for further studies. This is another evidence that the exciton-phonon coupling is quite different for A and B excitons.

As shown in Figure 1(a-b), when the incident laser is resonant with A exciton, we found two Fano lineshape peaks close to SM21 in 2TL and SM32 in 3TL, respectively. We proposed that these Fano peaks are from the quantum interference between SMNN-1 modes and electronic continuum state. Exactly, as shown in Figure 3(a), we can still observe these series of layer-dependent Fano resonant SMNN-1 modes in all of 2-7TL WS2 samples. The peak intensities in 2-4TL WS2 are much stronger than in thicker samples. Depending on specific resonant exciton properties, different LBMs show different resonant behaviors. Only Raman active LBMNN-1 modes appears in B exciton resonance; both Raman active modes of LBMNN-1 and LBNN-3 (N$>$3) appear in C exciton resonance cases; interestingly, we can observed IR-active LBMNN-2 (N$>$2) and Raman-active LBMNN-3 (N$>$3) in A exciton resonance. Figure 3(c) shows a fitting result of 3TL WS2 spectrum in Figure 3(a). We should note that the asymmetry direction of Fano resonant peak SM32 is towards to higher energy side and gives a positive q. For the peak around 24 cm*-1*, its frequency is rather close to the SM31 mode than LBM32, and thus we use Lorentzian LBM32 and Fano SM31 lineshape to fit the spectra. We concluded all of observed peaks in the Figure 3(d). We found all of LBM frequencies agree the LCM calculation very well. The fitted frequencies of SM31 and SMNN-1 Fano peaks perfectly match the uncoupled phonon frequencies obtained by LCM, but they are little bit lower than the peak frequencies of corresponding Fano resonant modes. As mentioned previously, this is because the positive q of Fano resonance SMNN-1 and SM31 mode will lead blueshift of the uncoupled SM frequency based on Fano resonance peak function of $\omega_{Fano}=\omega_{0}+\gamma/q$. For LA Fano resonant peak in A exciton resonance, we still obtain the negative q and redshifted peak frequencies related to uncoupled LA mode.

Based on the group theoryZhao-nanoletter-2013 , we note that among the N-1 interlayer shear modes of the NTL crystal, only the modes with the jth-highest (j=1, 3, 5,…) frequencies (such as SM21, SM31, SM43) can be observed under both the parallel (VV) and VH polarization configurations. The jth-highest (j=2, 4, 6, …) frequency modes have a E*′′* symmetry (Raman-active) for odd-TLs (such as SM32, SM54 and SM76) and an Eu symmetry (IR-active) for even-TLs. However, these modes cannot be observed under back scattering geometry even though being Raman-active. Similarly, only the interlayer breathing modes with the jth-lowest (j=1, 3, 5, …) frequencies (such as LBMNN-1, LBMNN-3) are Raman-active and can be observed under the VV polarization configuration, while the one with the jth-lowest (j=2, 4, 6, …) frequencies (such as LBMNN-2) are all exclusively IR-active modes, with symmetries of $A^{\prime\prime}_{2}$ for odd-TLs and A2u for even-TLs. However, in our RRS experiments, we not only observed these backscattering forbidden phonon modes (SM32, SM54 and SM76), but also IR-active LBMNN-2 modes. We will discuss the physics behind these phenomena in section of discussion.

Instead of varying the excitation energies and sample layer numbers, we also conducted the RRS experiments by changing the sample temperature from 4 to 300 K. Figure 4(a) shows the temperature dependence of RRS spectra in 3TL WS2 excited by 2.41 eV laser, which is close to the B exciton transition of 3TL WS2 around 110 K. Both of the TA and LA modes show resonant enhancement behaviors when the B exciton transition is close to the excitation laser energy, but the SM31 mode shows non-resonant behavior that the intensity gradually decreases with decreasing temperature. More interesting, as shown in Figure 4(b) spectra excited by 2.03 eV laser, two Fano peak gradually emerge bellow 200 K and become more and more resolvable with decreasing temperature further. Here the laser energy of 2.03 eV is close to the A exciton transition of 3TL WS2 at 30 K. By comparing the LCM predicted frequencies of SM32 and SM31, we definitely confirm that these two peaks are from the Fano resonance between SM32, SM31 and electronic continuum state, respectively. When the temperature is higher than 200 K, A exciton transition red shifts to lower energy closed to 1.96 eV and the SM32 and SM31 Fano resonance profiles are replaced by acoustic phonon TA dominated profile as shown in Figure 4(b). This is consisted with spectra excited by 2.03 eV as shown in Figure 1(a-b). In Figure 4(c), we concluded the fitting parameters of $1/\emph{q}$ and $\gamma$ for SM32 and SM31 modes as a function of temperature. Since both of $1/\emph{q}$ values SM32 and SM32 Fano modes are almost the same, and thus we only show the $1/\emph{q}$ value of SM32. The value of $1/\emph{q}$ increases with temperature decreases below 30K and then decreases with temperature increases from 30 to 300 K. It indicates that the strongest coupling between phonons and electronic continuum happens at 30 K, where the A exciton transition energy is exactly resonant with excitation laser. The phonon linewidths of ${\gamma}$ are monotonically broadening with temperature increases due to arharmonic effects of phonons and relaxations of excitonslinewidth-prb-1984 ; RICHTER-SSC-1981 .

Besides observations of forbidden phonon modes in ultra-low frequency range, at low temperature, we also found another type of Raman forbidden but IR-active high frequency modes at A exciton resonance. We conducted the Raman spectra of 2-4TL WS2 excited by 2.03 eV from 4 to 300 K. Figure 5(a) exhibits that N Raman peaks are observed in NTL WS2 (N=2, 3, 4) around $\sim$ 420cm*-1*. These Raman modes become more and more resolvable with decreasing sample temperature, as shown in Figure 5(b). Moreover, as shown in Figure 5(c), these splitting modes show strongly intensity enhancement at A exciton resonant excitation. Based on the peak frequencies and peak numbers, we can definitely assign them as Davydov splitting components of A${}^{\prime}_{1}$-like modes in 2-4TL WS2, respectively. In NTL 2H MX2 samples, each normal mode of 1TL will turn into N Davydov splitting modes, keeping the intra-TL displacement while varying the phase difference (0∘ or 180∘) between adjacent TLsmote2-prb-2016 . These Davydov components are either Raman or IR-actived. Their total number is equal to the layer number. Therefore, all the Raman (R) and infrared (IR) active Davydov components of A${}^{\prime}_{1}$-like modes are observed in our experiments for 2-4TL, as labeled in Figure 5(a). Although the Davydov splitting has been observed in few-layer MoTe2mote2-prb-2016 ; Froehlicher-nanoletter-2015 , MoSe2Tonndorf-oe-2013 ; kim-nanoletter-2016 , and twisted grapheneWu-nc-2014 , the IR active components are still rarely reported. Recently, Staiger et al reported an experimental observation of IR-active and Raman-active Davydov components in few-layer WS2Staiger-prb-2015 by using resonant Raman scattering at room temperature, but the spectra are not resolved very well and it is not clear why IR-active phonons can be observed in Raman scattering. Here, by using the RRS at low temperature, we can clearly resolve all of Davydov components of A${}^{\prime}_{1}$-like modes in 2-4TL WS2, including the Raman active A${}^{\prime}_{1}/A_{1g}$ and IR active A${}_{2u}/A^{\prime\prime}_{2}$ modes.

Discussions

So far, several forbidden phonon modes have been observed in RRS spectra of few-layer WS2, including IR-active phonons (low frequency LBMNN-2, and high requency A${}_{2u}/A^{\prime\prime}_{2}$ modes) and Raman-active but backscattering forbidden phonons (SM32, SM54 and SM76). Besides, the LA mode shows a Fano lineshape with negative q in both of A and B exciton resonance, and the peak intensity is much stronger in B exction resonance than in A exciton resonance; the SMNN-1 and SM31 show the positive q Fano lineshape only under A exciton resonance. In RRS, the observation of backscattering forbidden phonons can be explained by Fr$\ddot{o}$hlich mechanism of exction-phonon interactionPhysRevLett-26-86 . In RRS, Fr$\ddot{o}$hlich interaction between excitons and phonons leads to the forbidden scattering intensity is proportional to $(\emph{k}_{p}a)^{2}$, where $\emph{k}_{p}$ is wave vector of phonon and a is a Bohr radius of the exciton. Thus, forbidden phonons are observed only if a is much larger than the lattice constant. In this case, forbidden phonons in backscattering get the largest scattering cross-section because $\emph{k}_{p}$ is the largest in backscattering. These conditions can be satisfied in WS2 because the excitons in WS2 are large-radius Wannier excitonsDark-exciton-nature-2014 and they can couple to phonons via the intraband Fr$\ddot{o}$hlich interaction.

The observation of IR-active phonon in our RRS experiments can be explained by analyzing the RRS process. The first-order resonant Raman scattering probability is given bycu2o-prl-1974 ; PhysRevLett-3141-1973 :

[TABLE]

where ${\omega_{i}}$, ${\omega_{ph}}$ and $\omega_{s}=\omega_{i}\pm\omega_{ph}$ is the incident photon, phonon and scattering photon frequencies, and $m^{\prime}$ and $m$ are intermediate exciton state with energy E${}_{m^{\prime}}$ and E${}_{m^{\prime}}$ and widths $\gamma_{m^{\prime}}$, and ${\gamma_{m}}$, respectively. ${H_{eL}}$ denotes the exciton-lattice interaction; ${H_{eR}}$ denotes the exciton-radiation-field interaction.

In few-layer WS2, the spin-orbit splitting of conduction band leads to both of 1s A and B exciton split into dark and bright exctonic fine structures, respectively. Bright state has odd parity and is dipole (E1) transition allowed; dark state has even parity and is dipole forbidden but electric quadrupole (E2) or magnetic dipole (M1) allowedZhangXX-prl-2015 ; Splitting-PRB-2016 . Beside excitons, phonons also have definite parity based on group theory: IR-active phonons have odd parity but Raman-active phonons have even parityDMS-1984 . Since exction-phonon interaction $H_{eL}$ has the same symmetry with scattered phonons, the parity of $H_{eL}$ is the same as the parity of phonons. In order to get a nonzero transition in equation (2), the parity of $H_{eL}$ has to be the same as parity of $H_{eR}{(\omega_{i})}\otimes{H_{eR}{(\omega_{s})}}$ cu2o-prl-1974 ; PhysRevLett-3141-1973 . In non-resonant or bright exciton resonant condition, since both of $H_{eR}{(\omega_{i})}$ and $H_{eR}{(\omega_{s})}$ are electronic-dipole allowed E1 transitions with odd parity, and thus the product of ${H_{eR}{(\omega_{i})}}\otimes{H_{eR}{(\omega_{s})}}$ is even parity. Therefore, a nonzero transition in equation (2) is required that the $H_{eL}$ (and thus phonons) must be even parity (Raman-active). This is equivalent to the classical statement that a phonon is Raman active in first order Raman scattering only when its parity is even. When the dark exciton involved in the resonant Raman transition, for example, the incident resonance case, the ${H_{eR}(\omega_{i})}$ is E2 or M1 transition with even parity and the off-resonant out-going transition ${H_{eR}(\omega_{s})}$ is the usual E1 transition with odd parity, and thus the product of $H_{eR}{(\omega_{i})}\otimes{H_{eR}{(\omega_{s})}}$ is odd parity. Therefore, the phonons related to $H_{eL}$ must be odd parity (IR-active). It has the same result in out-going resonant transition. In conclusion, when the incident or scattering photons resonate with odd-parity dark-excitons, odd parity IR-active phonons can be observed based on the parity selection rule of Raman scattering. This mechanism, therefore, explains why the odd parity IR-active modes can be involved in RRS in few-layer WS2.

Another factor to affect the Raman intensity in equation (2) is damping constant of intermediate exciton states. Normally one expects the E2 and M1 transition matrix elements in Eq. (2) to be several orders of magnitude weaker than the E1 transition matrix elements. Generally, such forbidden IR-active phonon modes should be too weak to be observed. However, the small optical matrix elements result in small radiative decay probabilities and hence small damping constants $\gamma_{m^{\prime},m}$ of intermediate excitons. At resonance, the small damping constant of dark excitons in the denominators in Eq. (2) over-compensates the small matrix elements in the numerator, because the damping constants are proportional to the square of the optical matrix elements. Since damping constants are inverse proportional to the lifetime, this means dark excitons have much longer life-time than bright excitons. This is particularly true for 1s excitons in TMDs. For example, the lifetime of dark exciton is in the order of from nanosecond in monolayer TMDsZhangXX-prl-2015 ; trion-NC-2016 to microsecond in 2D heterostructuresXiong-arXiv-2017 , which are much longer than that of the bright exciton in an order of picosecond in TMDs. Besides, we should note that the IR-active modes and Fano lineshape SMs only are observed under A exciton resonance but vanished under B exciton resonance. This is because the oscillator strength of A and B dark excitons are very different. Although the oscillator strength of A exciton dark state is quite small, but it is not strictly zero because its single particle state can be slightly mixed with remote bandsXD-prl-2012 ; Splitting-PRB-2016 . However, for dark B-exciton state, its symmetry can be represented as $\Gamma_{6}$. Therefore, the oscillator strength of dark B-exciton is strictly equal to zeroSplitting-PRB-2016 . This is the reason why we could almost not observe IR-active modes and Fano lineshape SMs under B exciton transitions. Comparing the other techniques used to detect the excitonic dark states in few-layer TMDsDark-exciton-nature-2014 ; ZhangXX-prl-2015 ; trion-NC-2016 , our RRS technique can simultaneously detect the forbidden phonons and dark exciton states.

Now let’s discuss physical mechanisms behind the Fano resonance of SMNN-1, SM31 and $LA$ modes. Figure S5 in supplementary information presents the schematic diagram of dark-bright energy splitting of the 1s A excitons in WS2 systems at K pointSplitting-PRB-2016 . We should note linewidthes of bright and dark excitons are much broader than that of phonons, and even larger than the phonon energies involved in Fano resonance. In this case, the excitons act like a continuum state and phonon is discrete state. When the incident laser energy resonates with exciton transition, the laser-induced excited state will be populated and interferences with discrete phonons. Depending on the exciton-phonon coupling strength, some of phonons will show Fano resonance. There are two types of interferences between discrete phonon and continuum exciton states: one type is interband transition involved k$\simeq$0 phonon; the other one is intraband or interband transition involved k$\neq$0, where intraband transition is spin conservation and interband transition is accompany by spin-flip scattering. From our experiments, we found that when the excitation energy (for example, 1.92 and 1.96 eV) is slightly lower than the bright A exciton transitions at room temperature, the Fano peaks of SMNN-1 are much stronger than that excited by 2.03 eV laser, which is slightly higher than the A exciton transitions, as shown in Figure 3(b,c) and supporting Figure S6. This result indicates that the exciton continuum must be below the bright exciton state. This proposal also can be further confirmed by measuring the Raman spectra from 4 to 300K with excitation energy of 2.03 eV. When temperature is above 200K, the Fano-type SMs almost vanished because the excitation energy is slightly larger than the A exciton transitions at room temperature. According to our experiments, the Fano lineshape of SMs appeared at a range from 1.92 eV to 1.96 eV at room temperature. Therefore, we can estimate dark-bright splitting of 1s A exciton is around -40 meV, which has the same sign but the splitting energy is larger than recent calculations of -20 meVNC-darkexciton-2017 and -11 meVSplitting-PRB-2016 . For B exciton, we can’t identify the bright-dark splitting based our results.

CONCLUSIONS

In conclusion, by studying the exctonic RRS spectra in few-layer and bulk WS2 excited by multiple wavelength laser lines, and at different sample temperatures from 4 to 300 K, we have observed several forbidden phonon modes that is unobservable in ordinary Raman scattering experiments. By analyzing the parity selection rule of Raman scattering and Fano resonance of SM and LA modes, we can not only explain our results very well, but also definitely determine the bright-dark fine structure of 1s A exciton. Our results not only provide a better understanding of exciton-phonon interactions, but also show alternative technique to simultaneously probe the dark excitons and forbidden phonons in few-layer TMDs. Besides, our experiment also presents an opportunity to study the strong many-body effects between light, excitons and phonons, and thus help the development of 2D materials in optoelectronic applications.

Methods

Sample preparation.

The samples were prepared from a bulk WS2 crystals onto a 90 nm SiO${}_{2}/$Si substrate and SiO2 substrate by using the micromechanical exfoliation technique.

Raman and Reflectance contrast $\Delta{R/R}$ measurements.

Raman measurements were undertaken in backscattering geometry with a Jobin-Yvon HR800 system equipped with a liquid-nitrogen-cooled charge-coupled detector. The spectra were collected with a 100 x objective lens (NA=0.9) and an 1800 lines mm*-1* grating at room temperature, while a 50 x long-working-distance objective lens (NA=0.5) was used at low temperature measurements. The excitation laser (EL) lines of 2.71 eV, 2.54 eV and 2.41 eV are from an Ar*+* laser; the laser lines of 2.09 eV, 2.03 eV and 1.96 eV are from a He-Ne laser; the laser lines of 2.34 eV, 2.18 eV, 1.92 eV and 1.83 eV are from a Kr*+* laser, the laser line of 2.81 eV is from a He-Cd laser. The ultralow-frequency Raman spectra were obtained down to $\pm$5 cm*-1* by combining three volume Bragg grating filters into the Raman system to efficiently suppress the Rayleigh signal. In order to avoid the laser heating effect to the samples, the laser power was kept below a maximum of 0.3 mW. The Montana cryostat system was employed to cool the samples down to 4K under a vacuum of 0.4 mTorr. The reflectance contrast $\Delta{R/R}$ were undertaken with a 100x objective lens (NA=0.9) and an 100 lines mm*-1* grating with white light at room temperature.

Acknowledgements

J.Z. and P.T. acknowledge support from National Basic Research Program of China (grant no. 2016YFA0301200), NSFC (11574305, 51527901, 11474277, 11434010 and 11225421) and and LU JIAXI International team program supported by the K.C. Wong Education Foundation and the Chinese Academy of Sciences. J. Z. also acknowledges support from National Young 1000 Talent Plan of China; Q.X. acknowledges Singapore National Research Foundation via NRF Investigatorship Award (NRF-NRFI2015-03), and the Singapore Ministry of Education via AcRF Tier 2 grant (MOE2012-T2-2-086 and MOE2015-T2-1-047).

Author contribution

J.Z. conceived the ideas; Q.T., P.T., Y.Z., and J. Z. designed the experiments. Q.T., Y.S. prepared the samples. Q.T., X.L. and Y.Z. performed experiments; Q.T., P.T. and Z.J. analyzed the data; Q.T., and Z.J. wrote the manuscript with input from all authors. J. Z., P.T. and Q.X. supervised the projects.

Additional information

Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to P.T.( Email: phtan@semi.ac.cn) and J.Z.(Email: zhangjwill@semi.ac.cn).

Competing interests: The authors declare no competing financial interest.

References

Supplementary Information