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Effects of Excitonic Resonance on Second and Third Order Nonlinear Scattering from Few-Layer MoS 2
Naveen Kumar Balla, Maria O'Brien, Niall McEvoy, Georg S. Duesberg, Herve Rigneault, Sophie Brasselet, and David McCloskey ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b00912 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on January 25, 2018
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Effects of Excitonic Resonance on Second and Third Order Nonlinear Scattering from Few-Layer MoS2 Naveen K. Balla1, Maria O’Brien2,3, Niall McEvoy2,3, Georg S. Duesberg3,4, Hervé Rigneault1 Sophie Brasselet1, David McCloskey2,5,*. 1Institut Fresnel, CNRS, Aix-Marseille Université, Ecole Centrale Marseille, Domaine Universitaire St Jérôme, 13013 Marseille, France. 2Centre for the Research on Adaptive Nanostructures and Nanodevices (CRANN) and Advanced Materials and BioEngineering Research Institute (AMBER), Trinity College Dublin, Dublin 2, Dublin, Ireland. 3School of Chemistry, Trinity College Dublin, College Green, Dublin 2, Ireland. 4Institute of Physics, EIT 2, Faculty of Electrical Engineering and Information Technology, Universität der Bundeswehr München, Werner-Heisenberg- Weg 39, 85577 Neubiberg, Germany. 5School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland. *
[email protected] Abstract Nonlinear optical scattering from single- and few-layer MoS2 contains important information about the orientation, inversion symmetry, and degree of interlayer coupling between the layers. We simultaneously map second harmonic generation (SHG) and four wave mixing (FWM) signals in chemical vapor deposition (CVD) grown 2H-phase MoS2 from single to 5 layers. We tune the excitation wavelengths to compare cases where the non-linear signals are on and off resonance with the A-exciton band. The SHG signal shows the expected 4-fold symmetry however, the FWM signal depends on the incident laser polarization only, and is independent of the crystallographic orientation. We show using the symmetry of the χ(3) tensor that this results from out of plane FWM dipoles. We explore the scaling of SHG and FWM signals with layer number on and off excitonic resonance When a nonlinear scattered signal overlaps with the A excitonic band, the scaling of the signals with layer number deviates from the expected values, due to the layer dependent red shift in the exciton absorption peak due to interlayer coupling. Finally we show that circularly polarized excitation significantly enhances nonlinear scattering which overlaps with the A excitonic band and indicates the presence of spin splitting of valence bands at the energy degenerate points (K, K’) of the Brillouin zone. Keywords: Second harmonic generation, four wave mixing, polarization resolved imaging, 2D materials, transition metal dichalcogenides. Experimental realization of two dimensional atomically layered materials has opened up new design strategies in materials science1. The optical and electronic properties of few-layer transition metal dichalcogenides (TMDs) are strongly dependent on layer number2,3, crystal phase4, and stacking angle through interlayer coupling5. This results in the well-known transition from indirect to direct bandgap in single-layer MoS26. Understanding the interactions between layers is therefore critical for design and operation of devices based on fewlayer 2D materials and artificially-stacked monolayers. Linear and non-linear optical techniques such as Raman scattering2, photoluminescence mapping3, SHG7–9, third harmonic generation (THG)10,
nonlinear absorption11,12 and FWM13 have proven to be invaluable tools in understanding the physics of few-layer 2D materials and devices. The peak position and the ratio of the E2g to A1g Raman peaks are commonly used to uniquely identify layer number2. Photoluminescence with electrical gating gives insight into neutral and charged exciton dynamics14. Polarization dependent second harmonic generation is strongly dependent on crystal symmetry7–9,15 and stacking orientation in few-layer TMDs5,16 and heterojunctions. A unique aspect of 2D materials is the existence of extremely strong excitonic effects even at room temperature due to reduced Coulombic screening17. Excitons in few-layer MoS2 have strong binding energies of 0.5 eV single layer and can have wave
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functions localized to less than 1 nm18. The exciton lifetime is reduced compared to bulk with transient absorption spectroscopy showing tri-exponential decays due to fast trapping by surface defects (2 ps), carrier phonon scattering (~20 ps) and electron hole recombination (~200 ps)18. The A and B excitonic features dominate the optical PL in the region of 600-700 nm. MoS2 monolayers lack inversion symmetry and exhibit spin splitting of valence bands due to spin-orbit coupling around the energy degenerate corners (K, K’) of the Brillouin zone19–21 Excitons in these valleys can be selectively excited by using circularly polarized light22,23. This important phenomenon allows room temperature optical manipulation of the valley degree of freedom. Valley coherence has been demonstrated experimentally by polarization and time-resolved photoluminescence (PL) measurements22,23. In this work we use spatially-resolved second and third order non-linear scattering to investigate the influence of the excitonic resonance nonlinear scattering in few-layer CVD-grown 2H-phase MoS2. We show the expected 4-fold symmetry in the second order scattering processes, however the 3rd order scattering process depends only on the laser polarization. We examine the scaling of the SHG and FWM signals with layer number on and off resonance with A-exciton. In 2H-phase MoS2 flakes, A excitons have different effects on the scaling of SHG and FWM signals with layer number. To demonstrate the involvement of A excitons in non-linear scattering we compared linearly and circularly polarized excitations. We show that circularly polarized excitation enhances resonant nonlinear signal which is due to spin orbital coupling of A excitonic transitions at energy degenerate points (K, K’) of the Brillouin zone.
polarization resolved nonlinear optical microscope (see Methods and Fig. S2). A Ti:Sapphire femtosecond laser was used to pump an optical parametric oscillator (OPO). Lasers of wavelengths 830 nm and1065 nm were overlapped in time and space in a 250 nm focal spot using a 1.15NA water immersion objective. The laser powers were maintained in the range of 1.5-2.0mW to reduce damage on the sample during the scanning. Three kinds of non-linear signal were collected for imaging and analysis – SHG from the pump laser (@415 nm), sum frequency generation (SFG) from mixing of pump and OPO (@466 nm) and FWM (@680 nm) involving two photons from the pump and one from the OPO. Spectra of nonlinear scattering are used to confirm these signals (Fig.S3).
Results and Discussion Second and third order scattering Single- and few-layer MoS2 was synthesized using a chemical vapor deposition (CVD) method (see Methods). All the samples of MoS2 studied here have 2H crystal phase, and layer number (sample thickness) was determined using photoluminescence (PL) and Raman microscopy (Fig. S1). Spatially resolved non-linear scattering studies on the identified areas were conducted using a custom built
Fig 1. (a) Schematic of non-linear scattering. Incident light of wavelengths 830 nm and 1065 nm gets converted to SHG at 415 nm, SFG at 466 nm and FWM at680 nm. (b) PL map showing single and bilayer areas. Second order scattering - (c) SHG and (d) SFG, respectively occurs in monolayer only. Bilayer is dark due to restoration of inversion symmetry. Third order scattering – (e) FWM. Signal increases with increasing layer number. Scale bar: 3 μm.
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Layer thickness predicted by Raman and PL mapping agrees well with contrast obtained with nonlinear optical microscopy of MoS2 samples (Figs. 1 & S1). Incident beams are collinearly polarized and no analyzer is used. The signals are collected in epidetection configuration. The nonlinear signals are spectrally filtered and recorded using photomultiplying tubes (PMTs). All images are recorded simultaneously so that we can compare the spatial distribution of intensities and scaling of signals with thickness of flakes. Second order scattering (SHG, SFG) is observed only from MoS2 flakes with an odd number of layers because they lack inversion symmetry8,9. Third order scattering (FWM), on the other hand, is observed from both the single and bilayers, and increases with increasing layer number13. Symmetry of Scattering To further analyze the samples, polarization resolved imaging24 was performed using the forward detection pathway. The dichroic beam splitter in the epi-detection path distorts signal polarization25 and therefore it is not suitable for polarization-resolved measurements. Forward detection was used only to preserve the polarization of the scattered signal for analysis. The linear polarization of the co-polarized lasers was rotated in steps of 10° from 0°-170° using a half wave plate (HWP) mounted on a motorized rotation stage (Fig. S2). An analyzer was used in the detection pathway with polarization axis fixed at 0o. The MoS2 monolayer has D3h crystal symmetry, resulting in a second order nonlinear susceptibility tensor ( χ(2) ) with nonzero elements dyyy, dyxx, dxxy and dxyx where x and y represent the crystal axes9,26. Polarization-resolved analysis of SHG (Fig. 2a&c, Media1) and SFG (Fig. S4, Media2) signals yields 4fold symmetry which agrees with earlier reported results9 and theoretical calculations (See S.I., media1 & media2). Similar analysis of third order nonlinear scattering has not previously been performed in detail. A recent report suggests that polarization resolved analysis of the FWM signal from thin flakes of MoS2 yields a 6-fold symmetry13. However, our experimental results indicate that the polarization of FWM is dependent solely on the incident lasers’ polarization and not the orientation of MoS2 crystal axes (Fig. 2b&d, Media3). These results agree with polarization-resolved analysis of THG10,27 from MoS2,
which is another kind of third order scattering process like FWM. For a crystal with D3h symmetry, there can be 21 non-zero elements26 in the third order susceptibility tensor ( χ(3) ) but only the terms leading to axially oriented FWM dipoles yield to a FWM signal which is independent of a crystal’s planar orientation (See S.I.). Since the polarizationresolved analysis of FWM (Fig. 2) shows independence from planar orientation of MoS2 monolayers, the χ(3) matrix of thin MoS2 samples must be dominated by dzzzz, dzzyy, dzzxx, dzyyz, dzxxz, dzyzy and dzxzx elements. For detailed theoretical calculations please see supplementary information.
Figure 2. Polarizaton-resolved (a,c) SHG and (b,d) FWM microscopy of MoS2 monolayers with different incident linear polarizations and fixed analyzer (0°) in the detection path. For a given polarization of lasers (0° for a&b) simultaneously acquired (a) SHG and (b) FWM images show different intensity variations. Polar plots of intensities from three different flakes marked in (a) show that (c) SHG depends on orientation of the flakes and laser polarization whereas (d) FWM depends only on laser polarization. Scalebar: 5μm.
Exciton and Layer Number dependence Next we investigated the effect of layer number on the nonlinear scattered signal. The intensity (I) of the scattered nonlinear signal depends on the number of nonlinear scatterers (N), amplitude (Ei) and phase (ϕi) of the scattered signal from the ith scatterer (Eq. 1). In a MoS2 flake each layer can be considered as a scatterer. Ignoring strong interlayer coupling and depletion of incident light as it passes
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through a multilayered flake, amplitude of scattered signal (Ei) from each layer is the same (E) but the phase can vary. Under these assumptions, intensity of the scattered light can be approximated by equation (1). I ∝ E 2 ∑ cos(φi ) N
2
(1)
The scattered nonlinear signal from N layers adds in amplitude. If the scattered signal from the layers match perfectly in phase, intensity of the total signal scales as N2 and if the layers are perfectly out of phase, the intensity goes to zero (≡ N-∞). It is important to note that in the absence of coherence between scatterings from different layers, the signal from different layers is phase independent and the total intensity scales as N like in the case of fluorescence.
Figure 3 a) SHG and (b) FWM images of MoS2 flakes of varying thickness. Flakes of thickness 1-5 layers are marked in FWM image. (c) SHG intensity decreases gradually with increasing layer thickness whereas (d) FWM intensity increases rapidly with layer thickness. Scalebar: 5μm.
MoS2 flakes consisting of 1-5 layers were imaged with a combination of linearly polarized 830 nm and 1065 nm lasers. Layer number was identified using PL and Raman mapping (See S.I.). A stack of 18 images with different excitation polarization angles (0o-170o, step of 10o) was acquired and no analyzer was used in the detection path. Excitation polarization averaged SHG (Fig. 3a) and FWM (Fig. 3b) images were used to analyze signal intensity and layer thickness (Fig. 3c&d). The outline and layer thickness of these flakes is marked in figure 3(b).
The SHG signal from the 830 nm laser is detectable only from flakes with an odd number of layers and it decreases with increasing number of layers (Fig. 3c). The SHG signal from flakes with an even number of layers is very low (Fig. 3a&c). In a MoS2 flake with an odd number of layers, if we pair up adjacent layers which are opposite in orientation (only in the case of 2H-phase MoS2), the SHG from each pair is 0 because pairs form centrosymmetric structures but SHG from the last odd layer is finite. With increasing N, absorption of laser and SHG signal also increase and hence, the SHG from the unpaired layer decreases in magnitude. Taking into account absorption of laser and SHG signal in the thicker flakes, SHG from 3- and 5-layer flakes should drop by 29% and 49% respectively when compared to SHG from monolayer9. However, the sharp decrease in SHG observed here (Fig. 3c, 56% and 70% respectively for 3- and 5-layer flakes) cannot be completely explained by increased absorption of the laser and the SHG signal in thicker flakes9 and it can be argued that the layer number dependent optical properties are responsible for the sharp decline in SHG from thicker flakes with an odd number of layers. The slope of a linear curve between logarithmic values of layer number and acquired SHG signal is negative at -0.74 (Fig. 3c) due to increased absorption in the thicker layers and interlayer coupling. Please note that SHG from flakes with an even number of layers was not used in this fitting, but have been included in figure 3(c). An appreciable FWM signal, on the other hand, is observed from flakes of all thickness and it increases with layer number (Fig. 3b). The FWM signals from individual layers add up in phase which explains the rapid increase in FWM signal with flake thickness. Similar results were observed for SHG from 3Rphase MoS2 flakes28 in which the adjacent layers are parallel in orientation and therefore all flakes lack inversion symmetry. In the case of FWM, the slope is 2.32 (Fig. 3d) which is greater than the expected value of 2 when layers are scattering perfectly in phase but without interlayer coupling. Our results are in agreement with recently reported results on SHG from 3R-phase MoS228 where slopes greater than 2 were consistently recorded in the absence of excitonic resoanance. This value of the slope also indicates that absorption of laser and FWM signal is small in flakes which are up to 5 layers thick. These measurements were carried out away from excitonic resonances of MoS2 monolayers. MoS2 monolayers undergo A excitonic transition at around 652 nm6. SHG from a 1304 nm laser and FWM from the combination of 809 nm and 1065 nm lasers overlap with the A excitonic transitions in MoS2
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monolayers. The resonant SHG signal shows a gradual increase with layer number (Fig. 4a&b) which is in sharp contrast to the decay observed under non-resonant conditions (Fig. 3a&c). The slope for linear fit between logarithmic values of layer number and resonant SHG is 0.22. This is close to the expected value of 0 where only one odd layer effectively causes SHG, SHG due to adjacent pairs of layers in zero and there is no interlayer coupling. In the case of flakes with an even number of layers (side panels in Fig. 4a), finite SHG signal can be detected with respect to the background (Fig. 4b) and it shows more than an order of magnitude increase when compared to non-resonant SHG (Fig. 3c). This SHG signal from flakes with even number of layers is attributed to the imperfect cancellation of SHG9 from the adjacent layers. It also explains the value of slope (0.22) greater than 0. To the best of our knowledge, this is the first report of increased SHG from even number of 2H-phase MoS2 layers due to resonance with the A exciton.
Figure 4 a) Resonant SHG image of MoS2 flakes which shows detectable signal from flakes with an even number of layers (Side panels). (b) SHG intensity gradually increases with increasing number of layers. (c) FWM intensity also increases with increasing layer thickness. Scalebar: 5μm.
with increasing layer thickness causes different degrees enhancement for SHG for different layer thickness28. Though this argument explains scaling of resonant FWM signal with layer thickness in our case, it does not explain the scaling of resonant SHG from 2H-phase MoS2 which according to the same argument should have a slope of less than 0. We believe that in addition to the A excitons, interlayer layer coupling also plays a role here by changing the electronic properties of the flakes. Response to circularly polarized pump Due to the lack of inversion symmetry in MoS2 monolayers and the presence of strong spin-orbit coupling in TMDs, left and right circularly polarized light can be used to selectively excite interband transitions at K and K’ points, respectively21–23. Linearly polarized light at the A excitonic wavelength equally excites transitions at K and K’ points but circularly polarized light, depending on its handedness, excites transitions at either K or K’ points. Therefore circularly polarized nonlinear scattering (SHG and FWM), which originates from circularly polarized excitation in the case of MoS2 flakes, should be enhanced close to A excitonic transitions in MoS2 monolayers. The ratio of nonlinear scattering intensities with circularly and linearly polarized excitations should also be higher on resonance than off resonance from MoS2 flakes lacking inversion symmetry. Indeed we measured this ratio to be higher for both SHG and FWM at resonance than off resonance in flakes of thickness 1-5 layers (Fig. 5). In the case of SHG, the signal from flakes with an even number of layers was not considered because of low signal (Fig. 5a) and not because of their centrosymmetric structure. In the case of FWM, signal from all the flakes was analyzed (Fig. 5b). Photoselectivity of excitonic transitions with circular polarization even in centrosymmetric flakes can be explained on the basis of a decrease in the interlayer coupling at excitonic resonance and this has been demonstrated earlier in tungsten sulfide bilayers29 and molybdenum telluride bilayers30.
In the case of resonant FWM, the signal increase is more gradual with layer thickness (Fig. 4c) as compared to nonresonant FWM signal (Fig. 3d). The slope of linear fit between logarithmic values of layer number and resonant FWM is 1.73 which is a close match to similar measurements from resonant SHG observed from 3R phase MoS2 flakes28. In the case of resonant SHG from 3R-phase MoS2 flakes, it was argued that the red-shift in A excitonic resonance
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transitions which retain their spin selectivity even in multilayered structures. This is most likely due to weak interlayer coupling29,30. Given the similarities in electronic properties of TMDs, similar behaviors are expected in other TMDs. Non-linear microscopy is an important tool in understanding and characterizing the properties of few layer TMDs. This work adds further understanding to the interpretation of second and third order scattering in terms of symmetries, scaling with layer number and properties on and off excitonic resonance.
Figure 5. Resonance with A exciton influences nonlinear scattering of linear and circularly polarized excitations from MoS2 flakes. Both (a) SHG and (b) FWM signals show an enhancement with circularly polarized excitation at resonance from MoS2 flakes of different thickness (1-5 layers).
With circularly polarized excitation, the slope of linear fit between logarithmic values of signal and layer number does not change much, 1.78 for FWM and 0.20 for SHG which indicates that circular polarization does not significantly alter scaling of nonlinear signal with layer number. Conclusions In summary, we have simultaneously mapped second and third order nonlinear scattering processes in single and few layer MoS2. We have demonstrated that the third order nonlinear dipoles in thin flakes of MoS2 are predominantly normal to the surface of the flakes, and the polarization of the third order scattered signal is follows that of the excitation laser. We support this experimental result with a thorough tensor analysis of FWM in MoS2 monolayers. Secondly, we addressed the topic scaling of non-linear signals with MoS2 layer number. The scaling was shown to deviate significantly from expected trends when the non-linear signal is close to the A-excitonic transition. We believe that this is due to the red shift of the A exciton with increasing layer number as well as due to interlayer coupling but this has to be investigated in greater detail. Finally we demonstrate significant enhancement of resonant nonlinear scattering due to circular polarization indicating the involvement of interband
Methods MoS2 preparation Few layer MoS2 samples were synthesized as described previously31. Briefly, a suspension of MoO3 nanosheets32 in isopropyl alcohol was drop cast on SiO2 substrate. Then the substrates were heated to evaporate the solvent completely. Then the MoO3 samples with the substrate were placed in ceramic boat and the assembly was heated at 750°C in a quartz tube furnace under 150 sccm Ar flow. Sulphur vapors were introduced to the samples using Ar gas as a carrier for 20 min. Finally the samples were annealed at 750°C in Ar and cooled to room temperature. The final samples were transferred to glass coverslips using polymer support transfer technique31,33. Raman and PL spectroscopy Raman spectroscopy and photoluminescence measurements were performed using a confocal Raman microscope (alpha300R, WITec Wissenschaftliche Instrumente und Technologie GmbH) with a 532 nm excitation laser and a laser power of
