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Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS2

Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS2 Article This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. www.acsnano.org Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS Yunyun Dai,* Yadong Wang, Susobhan Das, Hui Xue, Xueyin Bai, Eero Hulkko, Guangyu Zhang, Xiaoxia Yang, Qing Dai, and Zhipei Sun* Cite This: ACS Nano 2020, 14, 8442−8448 Read Online Metrics & More Article Recommendations sı Supporting Information ACCESS * ABSTRACT: Monolayer transition-metal dichalcogenides show strong optical nonlinearity with great potential for various emerging applications. Here we demonstrate the gate-tunable interband resonant four-wave mixing and sum-frequency generation in monolayer MoS . Up to 80% modulation depth in four-wave mixing is achieved when the generated signal is resonant with the A exciton at room temperature, correspond- (3) ing to an effective third-order optical nonlinearity |χ | tuning eff −18 2 2 from (∼12.0 to 5.45) × 10 m /V . The tunability of the (2) effective second-order optical nonlinearity |χ | at 440 nm C- eff exciton resonance wavelength is also demonstrated from (∼11.6 −9 to 7.40) × 10 m/V with sum-frequency generation. Such a large tunability in optical nonlinearities arises from the strong excitonic charging effect in monolayer transition-metal dichalcogenides, which allows for the electrical control of the interband excitonic transitions and thus nonlinear optical responses for future on-chip nonlinear optoelectronics. KEYWORDS: nonlinear optics, four-wave mixing, sum-frequency generation, gate tunability, exciton, MoS tomically thin transition-metal dichalcogenides modern photonics, which is challenging with traditional NLO 26,29−31 (TMDs) have stimulated great interest due to their materials. However, the electrical control of the other 1,2 A favorable physical properties, such as extremely large NLO responses in TMDs still remains unexplored, although it exciton binding energy and valley pseudospin physics arising is highly desired for future applications. from a large spin−orbit interaction. In particular, TMD In this work, we report the interband excitonic effect of monolayers feature a direct band gap in the visible spectral 2,5 various nonlinear optical processes, including four-wave mixing range, enabling diverse photonic applications including 6 7 8 (FWM) and sum-frequency generation (SFG), in monolayer modulators, photodetectors, and light-emitting diodes. Furthermore, TMD monolayers have recently attracted a MoS at room temperature. We fabricate an ion-gel-gated surge of attention focusing on their fascinating optical monolayer MoS device for effective electron doping by 9 10−12 nonlinearities (e.g., harmonic generation and saturable applying positive gate voltages. We demonstrate the excitonic 13,14 absorption ), which are promising for various applica- 15 16,17 enhancement and the gate-tunable FWM of monolayer MoS . tions, such as wavelength conversion and ultrafast pulse 18−20 Similarly, for the SFG process, the enhancement and the generation. nonlinear optical tunability at the interband excitonic In TMD monolayers, the strongly bound and tunable 3,21,22 excitons enable the enhanced light−matter interac- resonance are also reported. Besides, the second- and third- 23,24 tion and tunable linear and nonlinear optical responses order nonlinear coefficients are calculated as a function of 25,26 on the atomic thickness scale. For example, it has been doping carrier densities. demonstrated that the strong interband excitonic effect results in the significant enhancement of various harmonic generation 27,28 Received: March 28, 2020 processes in TMD monolayers. Additionally, it has been Accepted: June 29, 2020 reported that second-harmonic generation in the WSe Published: June 29, 2020 monolayer can be electrically tuned at A-exciton resonance. The interband excitonic enhancement and the tunability of nonlinear optical (NLO) responses are fascinating for numerous applications and will enable the versatility of future https://dx.doi.org/10.1021/acsnano.0c02642 © 2020 American Chemical Society ACS Nano 2020, 14, 8442−8448 8442 ACS Nano www.acsnano.org Article Figure 1. Monolayer MoS device and its gate-tunable electrical and linear optical properties. (a) Schematic of the gated monolayer MoS 2 2 device with Ti/Au as source (S) and drain (D) electrodes. Ion gel is used as gate dielectric with Ti/Au as the gate (G) electrode. (b) Source- drain current of the MoS device as a function of the gate voltage V from −3 to 3 V with the source−drain bias voltage fixed at 0.1 V. Inset: 2 g The optical image of the monolayer MoS channel (white dashed box) with source−drain contacts (yellow regions) on the Si/SiO substrate. 2 2 Scaler bar: 20 μm. (c) Differential reflection spectra at different gate voltages and the reference linear absorption spectrum (gray) of monolayer MoS at zero gate voltage. A, B, and C excitons are labeled. Figure 2. Gate-tunable FWM in monolayer MoS . (a) Wavelength-dependent FWM spectra. Pump λ is at ∼800 nm with an average power of 2 1 ∼1 μW, and idler λ is tunable from ∼930 to 1120 nm with an average power of ∼1 μW. Inset: Schematic of the FWM of monolayer MoS . 1 2 FWM (ω , red arrow) is generated from monolayer MoS when it is excited by a pump light (ω , yellow arrow) and an idler light (ω , FWM 2 1 2 green arrow). (b) Diagram of the interband resonant FWM process with A(B) excitons. (c) Dependence of FWM peak intensities on incident light powers, with a fit of the experiment data to a power law I . Upper panel: Dependence of FWM on P with fit(s = ∼1.90). Lower panel: Dependence of FWM on P with fit(s = ∼0.93). (d) Gate-tunable FWM spectra resonant at the A exciton (∼650 nm) with λ = 800 2 1 nm and λ = 1040 nm. (e) Gate-tunable FWM spectra resonant at the B exciton (∼610 nm) with λ = 800 nm, λ = 1160 nm. (f) Normalized 2 1 2 FWM peak intensities as a function of gate voltage for FWM resonant at the A- (650 nm, red dots) and B- (610 nm, blue dots) excitonic states and off-resonance (700 nm, black dots). property of monolayer MoS is measured with different gate RESULTS AND DISCUSSION voltages. The transport curve is characteristic of an n-type Linear Optical Characterization in Monolayer MoS . A semiconductor, as shown in Figure 1b. Over a gate voltage schematic and an optical image of the MoS device are shown range (−3 to 3 V), the source−drain current increases with in Figure 1a,b. The device consists of a chemical-vapor- positive gating (i.e., V > 0.4 V), indicating effective electron deposited (CVD) monolayer MoS sheet on a SiO /Si 2 2 injection to MoS . The low off-current is due to the MoS - substrate, with Ti/Au (5/50 nm) as the source and drain 2 2 contact Schottky barrier. Note that in our experimental range electrodes. The ion-gel top-gate method is used for (i.e., the gate voltage range is between −3 and 3 V), we are not electrostatic gating, which changes the doping level and able to obtain effective hole doping. Therefore, in the following therefore the optical responses of MoS . By examination of the Raman and photoluminescence spectra (Figure S1), the CVD experiments, we mainly study the device at positive gating with MoS film is identified as a monolayer. Here the electrical effective electron doping. 8443 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article Figure 3. Gate-tunable SFG in monolayer MoS . (a) Wavelength-dependent SFG spectra. Inset: The diagram of interband resonant SFG (ω , red arrow) at the C exciton with excitations at ω (yellow arrow) and ω (green arrow). (b) Dependence of SFG peak intensities on SFG 1 2 incident powers, with a fit of the experiment data to a power law I . Upper panel: Dependence of SFG on P with fit(s = ∼0.92). Lower panel: Dependence of SFG on P with fit(s = ∼0.91). (c) Gate-tunable SFG spectra resonant at the C exciton (∼440 nm) when λ is at 800 2 1 nm and λ is at 980 nm. To understand the excitonic effect on the linear optical 2ω − ω ) from ∼1.77 to 2.00 eV (i.e., λ = ∼620−700 nm) 1 2 FWM properties, the reflection spectra of the MoS device are is studied, as shown in Figure 2a. The average power for both measured with electron doping at positive gating. The linear the pump and idler input light beams in the experiment is ∼1 absorption spectrum of monolayer MoS on a reference 2 μW (with a corresponding peak intensity of ∼44 GW/cm ). sapphire substrate shows pronounced absorption peaks We find that the FWM is enhanced at ∼650 nm when the attributed to A (∼650 nm), B (∼610 nm), and C (∼440 generated FWM photon energy (i.e., ℏω = ∼1.91 eV) FWM nm) excitonic transitions with no electrostatic gating (gray matches the A-excitonic energy of monolayer MoS , suggesting curve in Figure 1c). However, at a large gate voltage (e.g., V = the interband resonance at the A exciton (Figure 2b). 13 2 3 V with a doping carrier density of ∼4 × 10 /cm ), the We further study the interband resonant FWM at the A excitonic effect is strongly suppressed (Figure S2a). The carrier exciton. Here we use a pump light (ℏω )at ∼1.55 eV (i.e., λ = 1 1 density is estimated using the capacitor model N = C(V − ∼800 nm) and an idler light (ℏω )at ∼1.19 eV (i.e., λ = 2 2 V )/e, in which C is the ion-gel capacitance 2.45 μF/cm , e is on ∼1040 nm), and the generated FWM (ω =2ω − ω )isat FWM 1 2 the elementary charge, and V = 0.4 V is the turn-on voltage on ∼1.91 eV (i.e., λ = ∼650 nm). To examine the power FWM in the monolayer MoS device. Here we plot the differential dependence of the resonant FWM signal, the nonlinear optical RV() −R(3V) reflection spectra in Figure 1c, where R(V ) g spectra are measured when the power of the pump (P ) and R(3 V) idler (P ) light beams is changed, respectively. The upper panel represents the reflection of the monolayer MoS film on the of Figure 2c shows the peak intensities of the FWM spectra Si/SiO substrate at V . The differential reflection spectra 2 g with increasing P while P =1 μW. The lower panel of Figure clearly show a gate-tunable linear optical response at the A and 1 2 2c shows the peak intensities of FWM spectra with increasing B excitons. This is mainly because the injected carriers (e.g., P while P =1 μW. It roughly follows a square and linear electrons when V > 0.4 V) decrease the oscillator strength of 2 1 power-law behavior as a function of P and P , respectively, interband excitonic transitions: The higher the positive gate 1 2 voltage, the weaker the excitonic-transition-induced linear which confirms the two-color FWM process (ω =2ω − FWM 1 absorption will be. With a high enough gate voltage (e.g., V = ω ) involving the pump and idler light beams (details in the 3 V), the interband excitonic transitions could even be Supporting Information). We also study the gate-tunable switched off while a lower energy resonance known as trion resonant FWM in monolayer MoS with interband A-excitonic (e.g., A-) emerges (Figure S2b). The trion (A-) resonance is resonance, as shown in Figure 2d. The FWM intensities quite weak and is observable only by the derivative of the decrease significantly when V changes from 0 to 3 V. We reflection spectra. Therefore, the influence of trion is attribute the gate-tunable FWM to the modulation of the insignificant in our experiments at room temperature. Note oscillator strength of the interband excitonic resonance by the that a negligible change is observed at the C exciton, which is 26 gate-injected electrons. With increasing gate voltages, the consistent with the result discussed in ref 25. oscillator strength at the excitonic resonance decreases with Gate Control of Interband Resonant FWM in MoS . A increased doping (as shown in Figure 1c), thus suppressing the home-built femtosecond-laser-based microscopic system (Fig- exciton enhancement of nonlinear processes. As a result, the ure S3a) is employed for the nonlinear optical measurements FWM signals decrease with increasing gate voltage at the in monolayer MoS , as described in the Methods section. The excitonic resonant wavelength. Note that the gate-tunable monolayer MoS film, excited by two pump frequencies at ω 2 1 FWM results are repeatable (Figure S5). and ω (ω > ω ), typically generates various nonlinear optical 2 1 2 Similarly, with pump light (ℏω )at ∼1.55 eV (i.e., λ = 1 1 signals, for example, second-harmonic signals (2ω and 2ω ), 1 2 ∼800 nm) and idler light (ℏω )at ∼1.07 eV (i.e., λ = ∼1160 2 2 SFG (ω + ω ), and FWM (2ω ± ω , ω ± 2ω ), as shown in 1 2 1 2 1 2 nm), the generated FWM (ω =2ω − ω )at ∼2.03 eV Figure S4. FWM 1 2 (i.e., λ = ∼610 nm) is resonant with the B-excitonic state. Here we mainly study the FWM generation (inset of Figure FWM Figure 2e shows gate-tunable resonant FWM spectra at the B 2a): The pump light (ℏω )is fixed at ∼1.55 eV (i.e., λ = ∼800 1 1 exciton, where the FWM intensities also decrease with nm), and the idler light (ℏω ) is tunable in a near-infrared increased electrostatic doping due to the same operation spectral range from ∼1.1 to 1.33 eV (i.e., λ = ∼930−1120 nm). As a result, the wavelength-dependent FWM (ω = principle. FWM 8444 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article IV() FWM g is the repetition rate, τ = ∼230 fs is the estimated pulse (1,2,S,F) The normalized gate-tunable FWM ( ) is plotted in I (0 V) duration of the pump light beams and the SFG/FWM signals, FWM Figure 2f, where I (V ) is the peak intensity of FWM at V . D = ∼2.5 μm is the diameter of the laser spot with a FWM g g (1,2,S,F) Here we achieve a nearly 80% (70%) modulation depth Gaussian spatial profile, n = ∼4.2 is refractive index of (1,2,S,F) |− IV() I (0V)| FWM g FWM the material at the pump light frequencies and SFG/FWM ( ) when FWM is resonant at the A(B)- I (0 V) FWM frequencies, α = 2 for the two-color SFG process, α = 3 for S F 3/2 excitonic states with V tuning from 0 to 3 V. As a comparison, g the two-color FWM process, and φ =(π/ln 2) /8. Therefore, for the FWM at 700 nm (i.e., λ at 800 nm and λ at 920 nm), 1 2 the effective bulk-like second- and third-order nonlinear (2) (3) which is off excitonic resonance, gating does not change the coefficients of monolayer MoS (χ , χ ) can be obtained, 2 eff eff (2) (2) (3) (3) FWM intensity (black dots in Figure 2f). This further χ = χ /t and χ = χ /t, where t = ∼0.7 nm is the eff eff demonstrates the dominance of the interband excitonic effect thickness of the monolayer MoS . The detailed calibration and on the optical nonlinearity of monolayer TMDs. Note that the calculation method are discussed in the Supporting Informa- FWM remains constant when V < ∼0.4 V, which is due to the g tion. The typical average power of two pump light beams is ∼1 fact that the effective electron injection to MoS has a turn-on 2 μW for each light beam. When the gate voltage varies from 0 to threshold V at 0.4 V. This critical V is also indicated by the on on 3 V, corresponding to the carrier density change from 0 to ∼4 13 2 transport characteristics of monolayer MoS (Figure 1b). 2 × 10 /cm , the SFG signal at the C exciton changes from Gate Control of Interband Resonant SFG in MoS . We 2 ∼2.5 to 1.0 pW, and the FWM signal changes from ∼0.14 to also use the home-built femtosecond-laser-based microscopic 0.029 pW at the A exciton and from ∼0.093 to 0.028 pW at the (2) system to study SFG in monolayer MoS , as described in the 2 B exciton. Therefore, we obtain the gate-tunable |χ | and eff (3) Methods section. The SFG at the sum frequency (ω = ω + SFG 1 |χ | of monolayer MoS , as shown in Figure 4. The eff 2 ω ) is generated with the two input light beams at ω and ω . 2 1 2 In our SFG experiment, pump1 (ℏω )is fixed at ∼1.55 eV (i.e., λ = ∼800 nm), and pump2 (ℏω ) is tunable in the near- 1 2 infrared spectral range from ∼1.11 to 1.33 eV (i.e., λ = ∼930− 1120 nm). As a result, wavelength-dependent SFG is achieved from ∼2.66 to 2.88 eV (i.e., λ = ∼430−465 nm) (Figure SFG 3a). We find that SFG is enhanced at ∼440 nm, when the generated SFG photon energy (i.e., ℏω = ∼2.82 eV) SFG matches the C-excitonic energy of monolayer MoS (inset of Figure 3a). The enhancement suggests that the interband excitonic transition at the C exciton significantly contributes to Figure 4. Gate-tunable nonlinear coefficients in monolayer MoS . the enhanced SFG process. The power-dependent SFG signals (3) (a) Gate-tunable |χ | for FWM at the A and B excitons and (b) eff are examined (Figure 3b). The peak intensities of the SFG (2) gate-tunable |χ | for SFG at the C exciton. eff spectra scale linearly with pump1 power P (while pump2 power P = ∼1 μW) and P (while P = ∼1 μW), respectively, (3) −18 2 2 2 1 tunability of |χ | changes from (∼12.0 to 5.45) × 10 m / eff following the linear power-law behavior of SFG. 2 V at the interband A-excitonic resonance ((∼9.16 to 5.03) × We also study the gate-tunable SFG of MoS with interband −18 2 2 10 m /V at the interband B-excitonic resonance) as a C-excitonic resonance. The peak intensities of the resonant function of the doping carrier density (Figure 4a). Similarly, SFG at 440 nm decrease with increased electrostatic doping (2) the tunability of |χ | with the interband C-exciton resonance eff (Figure 3c), showing a nearly 60% modulation depth −9 at 440 nm changes from (∼11.6 to 7.40) × 10 m/V with |− IV() I (0V)| SFG g SFG ( )at V = 3 V, where I (V ) is the peak varying doping carrier density (Figure 4b). g SFG g I (0 V) SFG The calculated second- and third-order nonlinear coef- intensity of SFG at V . This demonstrates the gate tunability of (2) (3) −9 −18 ficients |χ | and |χ | are on the order of 10 and 10 eff eff the SFG process in monolayer MoS . 2 2 m /V , which are in the same range of previously reported Gate-Tunable Nonlinear Optical Coefficients. We have (2) −9 (3) −17 work (e.g., |χ | = ∼5 × 10 m/V in ref 36; |χ | = ∼10 eff eff realized the tunability of nonlinear optical signals, which arises −19 2 2 to 10 m /V in ref 12). Besides the electrical tunability, from the strong excitonic charging effects in monolayer MoS , different approaches have been developed to tune nonlinear allowing for exceptional control over the oscillator strengths at 37,38 optical responses of TMDs. For example, the strain- and the excitonic resonances. On the basis of the measured tunable plasmonic-antenna- induced tunability of the nonlinear FWM and SFG intensities, we can estimate the tunability of optical response has been studied in TMDs (fully discussed nonlinear coefficients of MoS . The second- and third-order (2) (3) in the Supporting Information). For further improvement, nonlinear coefficients χ and χ are calculated from the integrating monolayer MoS with waveguides, optical measured average powers of the incident light and the 41 31 fibers, or optical cavities will enhance light−matter generated nonlinear optical signals as follows interactions for higher light conversion efficiency. Besides, 2 2 gate-tunable optical nonlinearity at low temperature offers the 8nc φτf τ D D n n ε cP (2) S 12 1 2 12 0 S |χ |= 2 possibility for higher tunability and a better understanding of αω τDn PP SS SS S1 2 (1) the underlying physics. 2 2 8nc φτfD n ε c τDn P (3) F 11 10 22 2F |χ |= CONCLUSIONS αω P τ Dn P FF 1 (2) F F F2 The interband excitonic resonance of FWM and SFG is where P represents the average power of the two incident investigated in ion-gel-gated monolayer MoS at room (1,2,S,F) 2 pump beams and the generated SFG/FWM signals, f = 2 kHz temperature. The gate-tunable interband excitonic FWM and 8445 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article SFG are demonstrated by electrostatic doping, which AUTHOR INFORMATION originates from the modulation of the oscillator strength of Corresponding Authors interband excitonic resonances. For interband resonant FWM, Yunyun Dai − Department of Electronics and Nanoengineering, (3) |χ | of monolayer MoS changes from (∼12.0 to 5.45) × eff 2 Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000- −18 2 2 10 m /V at the A exciton (650 nm) and from (∼9.16 to 0002-1186-1864; Email: yunyun.dai@aalto.fi −18 2 2 5.03) × 10 m /V at the B exciton (610 nm). Similarly, the Zhipei Sun − Department of Electronics and Nanoengineering (2) tunability of |χ | with the interband C-exciton resonance at eff and QTF Centre of Excellence, Department of Applied Physics, −9 440 nm is tuned from (∼11.6 to 7.40) × 10 m/V, with the Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000- gate voltage varying from 0 to 3 V. Note that a similar 0002-9771-5293; Email: zhipei.sun@aalto.fi nonlinear optical tunability is anticipated for other TMDs (e.g., WS ). Therefore, our study is promising for electrically Authors controlled NLO devices based on 2D layered materials (e.g., Yadong Wang − Department of Electronics and 42 43 tunable saturable absorbers, on-chip nonlinear optics ), Nanoengineering, Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000-0001-8603-3468 extending the versatility of modern photonic systems. Susobhan Das − Department of Electronics and Nanoengineering, Aalto University, Fi-00076 Aalto, Finland METHODS Hui Xue − Department of Electronics and Nanoengineering, MoS Device Fabrication. The monolayer MoS is grown on a 2 2 Aalto University, Fi-00076 Aalto, Finland SiO /Si substrate by the CVD method. The source, drain and gate Xueyin Bai − Department of Electronics and Nanoengineering, electrodes were first patterned using electron-beam lithography Aalto University, Fi-00076 Aalto, Finland (Vistec) and then deposited with Ti/Au (5/50 nm) using electron- Eero Hulkko − Department of Electronics and Nanoengineering, beam evaporation. All electrodes were wire-bonded to a chip for Aalto University, Fi-00076 Aalto, Finland electrical control. Ion gel was spin-coated uniformly on the MoS Guangyu Zhang − Institute of Physics and Beijing National device. The ion-gel solution was prepared by dissolving 22 mg of Laboratory for Condensed Matter Physics, Chinese Academy of poly(styrene)-b-poly(ethylene oxide)-b-poly(styrene) (PS−PEO− PS) and 0.56 g of ion liquid ([EMIM][TFSI]) in 20 mL of Sciences, Beijing 100190, China; orcid.org/0000-0002- anhydrous dichloromethane. The ion liquid and dry dichloro- 1833-7598 methane were purchased from Sigma-Aldrich, and PS−PEO−PS was Xiaoxia Yang − Division of Nanophotonics, CAS Center for purchased from Polymer Source. Excellence in Nanoscience, National Center for Nanoscience and Nonlinear Optical Spectra Measurement. Ahome-built Technology, Beijing 100190, China femtosecond-laser-based microscopic system is employed for the Qing Dai − Division of Nanophotonics, CAS Center for nonlinear optical experiments. The schematic of this system is shown Excellence in Nanoscience, National Center for Nanoscience and in Figure S3a. Two incident light beams, with different frequencies, Technology, Beijing 100190, China; orcid.org/0000-0002- are linearly polarized with polarization directions parallel to each 1750-0867 other. Their typical spectra are shown in the Supporting Information. The pulse duration of the incident pulses is ∼230 fs, which is Complete contact information is available at: estimated by the cross-correlation measurement (Figure S3c). The https://pubs.acs.org/10.1021/acsnano.0c02642 pulses of the two pump light beams are spatially and temporally overlapped and focused collinearly on the sample, and they generate Author Contributions the nonlinear optical signals in the monolayer MoS film. The spectra Y.D. and Z.S. conceived the idea. Y.D. performed the of nonlinear optical signals are detected by a spectrometer (Andor, experiments with assistance from Y.W., S.D., H.X., X.B., and Hamamatsu) in the reflection configuration. The nonlinear optical E.H. on the device fabrication and characterization. G.Z., X.Y., signals of monolayer MoS were measured under different gate and Q.D. provided the CVD-grown MoS sample. Y.D. voltages. Note that when different source−drain voltages were applied, no change was observed in nonlinear optical signals. analyzed the experimental data. Y.D. and Z.S. wrote the Therefore, to fully exclude the electric-current-induced nonlinear manuscript with contributions from all authors. optical effects (e.g., current-induced second-order nonlinearity ), we Notes only apply gate-voltage and ground source and drain electrodes (i.e., The authors declare no competing financial interest. no source−drain current) in our experiments. ACKNOWLEDGMENTS ASSOCIATED CONTENT We acknowledge funding from the Aalto Centre for Quantum sı * Supporting Information Engineering, Business Finland (A-Photonics), Academy of The Supporting Information is available free of charge at Finland (grant nos. 276376, 284548, 295777, 304666, 312297, https://pubs.acs.org/doi/10.1021/acsnano.0c02642. 312551, and 314810), Academy of Finland Flagship Programme (grant no. 320167, PREIN), the European Union’s MoS film characterization, gate-tunable electrical and Horizon 2020 research and innovation program (Grant No. linear optical properties of monolayer MoS , FWM and 820423, S2QUIP), and ERC (grant no. 834742). SFG experiment setup and spectra of pump light, nonlinear optical spectra in monolayer MoS ,the REFERENCES repeatable gate-tunable FWM, gate-tunable SFG spectra (1) Manzeli, S.; Ovchinnikov, D.; Pasquier, D.; Yazyev, O. V.; Kis, A. with excitonic resonance and off-resonance, calculation 2D Transition Metal Dichalcogenides. Nat. Rev. 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Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS2

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Article This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. www.acsnano.org Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS Yunyun Dai,* Yadong Wang, Susobhan Das, Hui Xue, Xueyin Bai, Eero Hulkko, Guangyu Zhang, Xiaoxia Yang, Qing Dai, and Zhipei Sun* Cite This: ACS Nano 2020, 14, 8442−8448 Read Online Metrics & More Article Recommendations sı Supporting Information ACCESS * ABSTRACT: Monolayer transition-metal dichalcogenides show strong optical nonlinearity with great potential for various emerging applications. Here we demonstrate the gate-tunable interband resonant four-wave mixing and sum-frequency generation in monolayer MoS . Up to 80% modulation depth in four-wave mixing is achieved when the generated signal is resonant with the A exciton at room temperature, correspond- (3) ing to an effective third-order optical nonlinearity |χ | tuning eff −18 2 2 from (∼12.0 to 5.45) × 10 m /V . The tunability of the (2) effective second-order optical nonlinearity |χ | at 440 nm C- eff exciton resonance wavelength is also demonstrated from (∼11.6 −9 to 7.40) × 10 m/V with sum-frequency generation. Such a large tunability in optical nonlinearities arises from the strong excitonic charging effect in monolayer transition-metal dichalcogenides, which allows for the electrical control of the interband excitonic transitions and thus nonlinear optical responses for future on-chip nonlinear optoelectronics. KEYWORDS: nonlinear optics, four-wave mixing, sum-frequency generation, gate tunability, exciton, MoS tomically thin transition-metal dichalcogenides modern photonics, which is challenging with traditional NLO 26,29−31 (TMDs) have stimulated great interest due to their materials. However, the electrical control of the other 1,2 A favorable physical properties, such as extremely large NLO responses in TMDs still remains unexplored, although it exciton binding energy and valley pseudospin physics arising is highly desired for future applications. from a large spin−orbit interaction. In particular, TMD In this work, we report the interband excitonic effect of monolayers feature a direct band gap in the visible spectral 2,5 various nonlinear optical processes, including four-wave mixing range, enabling diverse photonic applications including 6 7 8 (FWM) and sum-frequency generation (SFG), in monolayer modulators, photodetectors, and light-emitting diodes. Furthermore, TMD monolayers have recently attracted a MoS at room temperature. We fabricate an ion-gel-gated surge of attention focusing on their fascinating optical monolayer MoS device for effective electron doping by 9 10−12 nonlinearities (e.g., harmonic generation and saturable applying positive gate voltages. We demonstrate the excitonic 13,14 absorption ), which are promising for various applica- 15 16,17 enhancement and the gate-tunable FWM of monolayer MoS . tions, such as wavelength conversion and ultrafast pulse 18−20 Similarly, for the SFG process, the enhancement and the generation. nonlinear optical tunability at the interband excitonic In TMD monolayers, the strongly bound and tunable 3,21,22 excitons enable the enhanced light−matter interac- resonance are also reported. Besides, the second- and third- 23,24 tion and tunable linear and nonlinear optical responses order nonlinear coefficients are calculated as a function of 25,26 on the atomic thickness scale. For example, it has been doping carrier densities. demonstrated that the strong interband excitonic effect results in the significant enhancement of various harmonic generation 27,28 Received: March 28, 2020 processes in TMD monolayers. Additionally, it has been Accepted: June 29, 2020 reported that second-harmonic generation in the WSe Published: June 29, 2020 monolayer can be electrically tuned at A-exciton resonance. The interband excitonic enhancement and the tunability of nonlinear optical (NLO) responses are fascinating for numerous applications and will enable the versatility of future https://dx.doi.org/10.1021/acsnano.0c02642 © 2020 American Chemical Society ACS Nano 2020, 14, 8442−8448 8442 ACS Nano www.acsnano.org Article Figure 1. Monolayer MoS device and its gate-tunable electrical and linear optical properties. (a) Schematic of the gated monolayer MoS 2 2 device with Ti/Au as source (S) and drain (D) electrodes. Ion gel is used as gate dielectric with Ti/Au as the gate (G) electrode. (b) Source- drain current of the MoS device as a function of the gate voltage V from −3 to 3 V with the source−drain bias voltage fixed at 0.1 V. Inset: 2 g The optical image of the monolayer MoS channel (white dashed box) with source−drain contacts (yellow regions) on the Si/SiO substrate. 2 2 Scaler bar: 20 μm. (c) Differential reflection spectra at different gate voltages and the reference linear absorption spectrum (gray) of monolayer MoS at zero gate voltage. A, B, and C excitons are labeled. Figure 2. Gate-tunable FWM in monolayer MoS . (a) Wavelength-dependent FWM spectra. Pump λ is at ∼800 nm with an average power of 2 1 ∼1 μW, and idler λ is tunable from ∼930 to 1120 nm with an average power of ∼1 μW. Inset: Schematic of the FWM of monolayer MoS . 1 2 FWM (ω , red arrow) is generated from monolayer MoS when it is excited by a pump light (ω , yellow arrow) and an idler light (ω , FWM 2 1 2 green arrow). (b) Diagram of the interband resonant FWM process with A(B) excitons. (c) Dependence of FWM peak intensities on incident light powers, with a fit of the experiment data to a power law I . Upper panel: Dependence of FWM on P with fit(s = ∼1.90). Lower panel: Dependence of FWM on P with fit(s = ∼0.93). (d) Gate-tunable FWM spectra resonant at the A exciton (∼650 nm) with λ = 800 2 1 nm and λ = 1040 nm. (e) Gate-tunable FWM spectra resonant at the B exciton (∼610 nm) with λ = 800 nm, λ = 1160 nm. (f) Normalized 2 1 2 FWM peak intensities as a function of gate voltage for FWM resonant at the A- (650 nm, red dots) and B- (610 nm, blue dots) excitonic states and off-resonance (700 nm, black dots). property of monolayer MoS is measured with different gate RESULTS AND DISCUSSION voltages. The transport curve is characteristic of an n-type Linear Optical Characterization in Monolayer MoS . A semiconductor, as shown in Figure 1b. Over a gate voltage schematic and an optical image of the MoS device are shown range (−3 to 3 V), the source−drain current increases with in Figure 1a,b. The device consists of a chemical-vapor- positive gating (i.e., V > 0.4 V), indicating effective electron deposited (CVD) monolayer MoS sheet on a SiO /Si 2 2 injection to MoS . The low off-current is due to the MoS - substrate, with Ti/Au (5/50 nm) as the source and drain 2 2 contact Schottky barrier. Note that in our experimental range electrodes. The ion-gel top-gate method is used for (i.e., the gate voltage range is between −3 and 3 V), we are not electrostatic gating, which changes the doping level and able to obtain effective hole doping. Therefore, in the following therefore the optical responses of MoS . By examination of the Raman and photoluminescence spectra (Figure S1), the CVD experiments, we mainly study the device at positive gating with MoS film is identified as a monolayer. Here the electrical effective electron doping. 8443 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article Figure 3. Gate-tunable SFG in monolayer MoS . (a) Wavelength-dependent SFG spectra. Inset: The diagram of interband resonant SFG (ω , red arrow) at the C exciton with excitations at ω (yellow arrow) and ω (green arrow). (b) Dependence of SFG peak intensities on SFG 1 2 incident powers, with a fit of the experiment data to a power law I . Upper panel: Dependence of SFG on P with fit(s = ∼0.92). Lower panel: Dependence of SFG on P with fit(s = ∼0.91). (c) Gate-tunable SFG spectra resonant at the C exciton (∼440 nm) when λ is at 800 2 1 nm and λ is at 980 nm. To understand the excitonic effect on the linear optical 2ω − ω ) from ∼1.77 to 2.00 eV (i.e., λ = ∼620−700 nm) 1 2 FWM properties, the reflection spectra of the MoS device are is studied, as shown in Figure 2a. The average power for both measured with electron doping at positive gating. The linear the pump and idler input light beams in the experiment is ∼1 absorption spectrum of monolayer MoS on a reference 2 μW (with a corresponding peak intensity of ∼44 GW/cm ). sapphire substrate shows pronounced absorption peaks We find that the FWM is enhanced at ∼650 nm when the attributed to A (∼650 nm), B (∼610 nm), and C (∼440 generated FWM photon energy (i.e., ℏω = ∼1.91 eV) FWM nm) excitonic transitions with no electrostatic gating (gray matches the A-excitonic energy of monolayer MoS , suggesting curve in Figure 1c). However, at a large gate voltage (e.g., V = the interband resonance at the A exciton (Figure 2b). 13 2 3 V with a doping carrier density of ∼4 × 10 /cm ), the We further study the interband resonant FWM at the A excitonic effect is strongly suppressed (Figure S2a). The carrier exciton. Here we use a pump light (ℏω )at ∼1.55 eV (i.e., λ = 1 1 density is estimated using the capacitor model N = C(V − ∼800 nm) and an idler light (ℏω )at ∼1.19 eV (i.e., λ = 2 2 V )/e, in which C is the ion-gel capacitance 2.45 μF/cm , e is on ∼1040 nm), and the generated FWM (ω =2ω − ω )isat FWM 1 2 the elementary charge, and V = 0.4 V is the turn-on voltage on ∼1.91 eV (i.e., λ = ∼650 nm). To examine the power FWM in the monolayer MoS device. Here we plot the differential dependence of the resonant FWM signal, the nonlinear optical RV() −R(3V) reflection spectra in Figure 1c, where R(V ) g spectra are measured when the power of the pump (P ) and R(3 V) idler (P ) light beams is changed, respectively. The upper panel represents the reflection of the monolayer MoS film on the of Figure 2c shows the peak intensities of the FWM spectra Si/SiO substrate at V . The differential reflection spectra 2 g with increasing P while P =1 μW. The lower panel of Figure clearly show a gate-tunable linear optical response at the A and 1 2 2c shows the peak intensities of FWM spectra with increasing B excitons. This is mainly because the injected carriers (e.g., P while P =1 μW. It roughly follows a square and linear electrons when V > 0.4 V) decrease the oscillator strength of 2 1 power-law behavior as a function of P and P , respectively, interband excitonic transitions: The higher the positive gate 1 2 voltage, the weaker the excitonic-transition-induced linear which confirms the two-color FWM process (ω =2ω − FWM 1 absorption will be. With a high enough gate voltage (e.g., V = ω ) involving the pump and idler light beams (details in the 3 V), the interband excitonic transitions could even be Supporting Information). We also study the gate-tunable switched off while a lower energy resonance known as trion resonant FWM in monolayer MoS with interband A-excitonic (e.g., A-) emerges (Figure S2b). The trion (A-) resonance is resonance, as shown in Figure 2d. The FWM intensities quite weak and is observable only by the derivative of the decrease significantly when V changes from 0 to 3 V. We reflection spectra. Therefore, the influence of trion is attribute the gate-tunable FWM to the modulation of the insignificant in our experiments at room temperature. Note oscillator strength of the interband excitonic resonance by the that a negligible change is observed at the C exciton, which is 26 gate-injected electrons. With increasing gate voltages, the consistent with the result discussed in ref 25. oscillator strength at the excitonic resonance decreases with Gate Control of Interband Resonant FWM in MoS . A increased doping (as shown in Figure 1c), thus suppressing the home-built femtosecond-laser-based microscopic system (Fig- exciton enhancement of nonlinear processes. As a result, the ure S3a) is employed for the nonlinear optical measurements FWM signals decrease with increasing gate voltage at the in monolayer MoS , as described in the Methods section. The excitonic resonant wavelength. Note that the gate-tunable monolayer MoS film, excited by two pump frequencies at ω 2 1 FWM results are repeatable (Figure S5). and ω (ω > ω ), typically generates various nonlinear optical 2 1 2 Similarly, with pump light (ℏω )at ∼1.55 eV (i.e., λ = 1 1 signals, for example, second-harmonic signals (2ω and 2ω ), 1 2 ∼800 nm) and idler light (ℏω )at ∼1.07 eV (i.e., λ = ∼1160 2 2 SFG (ω + ω ), and FWM (2ω ± ω , ω ± 2ω ), as shown in 1 2 1 2 1 2 nm), the generated FWM (ω =2ω − ω )at ∼2.03 eV Figure S4. FWM 1 2 (i.e., λ = ∼610 nm) is resonant with the B-excitonic state. Here we mainly study the FWM generation (inset of Figure FWM Figure 2e shows gate-tunable resonant FWM spectra at the B 2a): The pump light (ℏω )is fixed at ∼1.55 eV (i.e., λ = ∼800 1 1 exciton, where the FWM intensities also decrease with nm), and the idler light (ℏω ) is tunable in a near-infrared increased electrostatic doping due to the same operation spectral range from ∼1.1 to 1.33 eV (i.e., λ = ∼930−1120 nm). As a result, the wavelength-dependent FWM (ω = principle. FWM 8444 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article IV() FWM g is the repetition rate, τ = ∼230 fs is the estimated pulse (1,2,S,F) The normalized gate-tunable FWM ( ) is plotted in I (0 V) duration of the pump light beams and the SFG/FWM signals, FWM Figure 2f, where I (V ) is the peak intensity of FWM at V . D = ∼2.5 μm is the diameter of the laser spot with a FWM g g (1,2,S,F) Here we achieve a nearly 80% (70%) modulation depth Gaussian spatial profile, n = ∼4.2 is refractive index of (1,2,S,F) |− IV() I (0V)| FWM g FWM the material at the pump light frequencies and SFG/FWM ( ) when FWM is resonant at the A(B)- I (0 V) FWM frequencies, α = 2 for the two-color SFG process, α = 3 for S F 3/2 excitonic states with V tuning from 0 to 3 V. As a comparison, g the two-color FWM process, and φ =(π/ln 2) /8. Therefore, for the FWM at 700 nm (i.e., λ at 800 nm and λ at 920 nm), 1 2 the effective bulk-like second- and third-order nonlinear (2) (3) which is off excitonic resonance, gating does not change the coefficients of monolayer MoS (χ , χ ) can be obtained, 2 eff eff (2) (2) (3) (3) FWM intensity (black dots in Figure 2f). This further χ = χ /t and χ = χ /t, where t = ∼0.7 nm is the eff eff demonstrates the dominance of the interband excitonic effect thickness of the monolayer MoS . The detailed calibration and on the optical nonlinearity of monolayer TMDs. Note that the calculation method are discussed in the Supporting Informa- FWM remains constant when V < ∼0.4 V, which is due to the g tion. The typical average power of two pump light beams is ∼1 fact that the effective electron injection to MoS has a turn-on 2 μW for each light beam. When the gate voltage varies from 0 to threshold V at 0.4 V. This critical V is also indicated by the on on 3 V, corresponding to the carrier density change from 0 to ∼4 13 2 transport characteristics of monolayer MoS (Figure 1b). 2 × 10 /cm , the SFG signal at the C exciton changes from Gate Control of Interband Resonant SFG in MoS . We 2 ∼2.5 to 1.0 pW, and the FWM signal changes from ∼0.14 to also use the home-built femtosecond-laser-based microscopic 0.029 pW at the A exciton and from ∼0.093 to 0.028 pW at the (2) system to study SFG in monolayer MoS , as described in the 2 B exciton. Therefore, we obtain the gate-tunable |χ | and eff (3) Methods section. The SFG at the sum frequency (ω = ω + SFG 1 |χ | of monolayer MoS , as shown in Figure 4. The eff 2 ω ) is generated with the two input light beams at ω and ω . 2 1 2 In our SFG experiment, pump1 (ℏω )is fixed at ∼1.55 eV (i.e., λ = ∼800 nm), and pump2 (ℏω ) is tunable in the near- 1 2 infrared spectral range from ∼1.11 to 1.33 eV (i.e., λ = ∼930− 1120 nm). As a result, wavelength-dependent SFG is achieved from ∼2.66 to 2.88 eV (i.e., λ = ∼430−465 nm) (Figure SFG 3a). We find that SFG is enhanced at ∼440 nm, when the generated SFG photon energy (i.e., ℏω = ∼2.82 eV) SFG matches the C-excitonic energy of monolayer MoS (inset of Figure 3a). The enhancement suggests that the interband excitonic transition at the C exciton significantly contributes to Figure 4. Gate-tunable nonlinear coefficients in monolayer MoS . the enhanced SFG process. The power-dependent SFG signals (3) (a) Gate-tunable |χ | for FWM at the A and B excitons and (b) eff are examined (Figure 3b). The peak intensities of the SFG (2) gate-tunable |χ | for SFG at the C exciton. eff spectra scale linearly with pump1 power P (while pump2 power P = ∼1 μW) and P (while P = ∼1 μW), respectively, (3) −18 2 2 2 1 tunability of |χ | changes from (∼12.0 to 5.45) × 10 m / eff following the linear power-law behavior of SFG. 2 V at the interband A-excitonic resonance ((∼9.16 to 5.03) × We also study the gate-tunable SFG of MoS with interband −18 2 2 10 m /V at the interband B-excitonic resonance) as a C-excitonic resonance. The peak intensities of the resonant function of the doping carrier density (Figure 4a). Similarly, SFG at 440 nm decrease with increased electrostatic doping (2) the tunability of |χ | with the interband C-exciton resonance eff (Figure 3c), showing a nearly 60% modulation depth −9 at 440 nm changes from (∼11.6 to 7.40) × 10 m/V with |− IV() I (0V)| SFG g SFG ( )at V = 3 V, where I (V ) is the peak varying doping carrier density (Figure 4b). g SFG g I (0 V) SFG The calculated second- and third-order nonlinear coef- intensity of SFG at V . This demonstrates the gate tunability of (2) (3) −9 −18 ficients |χ | and |χ | are on the order of 10 and 10 eff eff the SFG process in monolayer MoS . 2 2 m /V , which are in the same range of previously reported Gate-Tunable Nonlinear Optical Coefficients. We have (2) −9 (3) −17 work (e.g., |χ | = ∼5 × 10 m/V in ref 36; |χ | = ∼10 eff eff realized the tunability of nonlinear optical signals, which arises −19 2 2 to 10 m /V in ref 12). Besides the electrical tunability, from the strong excitonic charging effects in monolayer MoS , different approaches have been developed to tune nonlinear allowing for exceptional control over the oscillator strengths at 37,38 optical responses of TMDs. For example, the strain- and the excitonic resonances. On the basis of the measured tunable plasmonic-antenna- induced tunability of the nonlinear FWM and SFG intensities, we can estimate the tunability of optical response has been studied in TMDs (fully discussed nonlinear coefficients of MoS . The second- and third-order (2) (3) in the Supporting Information). For further improvement, nonlinear coefficients χ and χ are calculated from the integrating monolayer MoS with waveguides, optical measured average powers of the incident light and the 41 31 fibers, or optical cavities will enhance light−matter generated nonlinear optical signals as follows interactions for higher light conversion efficiency. Besides, 2 2 gate-tunable optical nonlinearity at low temperature offers the 8nc φτf τ D D n n ε cP (2) S 12 1 2 12 0 S |χ |= 2 possibility for higher tunability and a better understanding of αω τDn PP SS SS S1 2 (1) the underlying physics. 2 2 8nc φτfD n ε c τDn P (3) F 11 10 22 2F |χ |= CONCLUSIONS αω P τ Dn P FF 1 (2) F F F2 The interband excitonic resonance of FWM and SFG is where P represents the average power of the two incident investigated in ion-gel-gated monolayer MoS at room (1,2,S,F) 2 pump beams and the generated SFG/FWM signals, f = 2 kHz temperature. The gate-tunable interband excitonic FWM and 8445 https://dx.doi.org/10.1021/acsnano.0c02642 ACS Nano 2020, 14, 8442−8448 ACS Nano www.acsnano.org Article SFG are demonstrated by electrostatic doping, which AUTHOR INFORMATION originates from the modulation of the oscillator strength of Corresponding Authors interband excitonic resonances. For interband resonant FWM, Yunyun Dai − Department of Electronics and Nanoengineering, (3) |χ | of monolayer MoS changes from (∼12.0 to 5.45) × eff 2 Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000- −18 2 2 10 m /V at the A exciton (650 nm) and from (∼9.16 to 0002-1186-1864; Email: yunyun.dai@aalto.fi −18 2 2 5.03) × 10 m /V at the B exciton (610 nm). Similarly, the Zhipei Sun − Department of Electronics and Nanoengineering (2) tunability of |χ | with the interband C-exciton resonance at eff and QTF Centre of Excellence, Department of Applied Physics, −9 440 nm is tuned from (∼11.6 to 7.40) × 10 m/V, with the Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000- gate voltage varying from 0 to 3 V. Note that a similar 0002-9771-5293; Email: zhipei.sun@aalto.fi nonlinear optical tunability is anticipated for other TMDs (e.g., WS ). Therefore, our study is promising for electrically Authors controlled NLO devices based on 2D layered materials (e.g., Yadong Wang − Department of Electronics and 42 43 tunable saturable absorbers, on-chip nonlinear optics ), Nanoengineering, Aalto University, Fi-00076 Aalto, Finland; orcid.org/0000-0001-8603-3468 extending the versatility of modern photonic systems. Susobhan Das − Department of Electronics and Nanoengineering, Aalto University, Fi-00076 Aalto, Finland METHODS Hui Xue − Department of Electronics and Nanoengineering, MoS Device Fabrication. The monolayer MoS is grown on a 2 2 Aalto University, Fi-00076 Aalto, Finland SiO /Si substrate by the CVD method. The source, drain and gate Xueyin Bai − Department of Electronics and Nanoengineering, electrodes were first patterned using electron-beam lithography Aalto University, Fi-00076 Aalto, Finland (Vistec) and then deposited with Ti/Au (5/50 nm) using electron- Eero Hulkko − Department of Electronics and Nanoengineering, beam evaporation. All electrodes were wire-bonded to a chip for Aalto University, Fi-00076 Aalto, Finland electrical control. Ion gel was spin-coated uniformly on the MoS Guangyu Zhang − Institute of Physics and Beijing National device. The ion-gel solution was prepared by dissolving 22 mg of Laboratory for Condensed Matter Physics, Chinese Academy of poly(styrene)-b-poly(ethylene oxide)-b-poly(styrene) (PS−PEO− PS) and 0.56 g of ion liquid ([EMIM][TFSI]) in 20 mL of Sciences, Beijing 100190, China; orcid.org/0000-0002- anhydrous dichloromethane. The ion liquid and dry dichloro- 1833-7598 methane were purchased from Sigma-Aldrich, and PS−PEO−PS was Xiaoxia Yang − Division of Nanophotonics, CAS Center for purchased from Polymer Source. Excellence in Nanoscience, National Center for Nanoscience and Nonlinear Optical Spectra Measurement. Ahome-built Technology, Beijing 100190, China femtosecond-laser-based microscopic system is employed for the Qing Dai − Division of Nanophotonics, CAS Center for nonlinear optical experiments. The schematic of this system is shown Excellence in Nanoscience, National Center for Nanoscience and in Figure S3a. Two incident light beams, with different frequencies, Technology, Beijing 100190, China; orcid.org/0000-0002- are linearly polarized with polarization directions parallel to each 1750-0867 other. Their typical spectra are shown in the Supporting Information. The pulse duration of the incident pulses is ∼230 fs, which is Complete contact information is available at: estimated by the cross-correlation measurement (Figure S3c). The https://pubs.acs.org/10.1021/acsnano.0c02642 pulses of the two pump light beams are spatially and temporally overlapped and focused collinearly on the sample, and they generate Author Contributions the nonlinear optical signals in the monolayer MoS film. The spectra Y.D. and Z.S. conceived the idea. Y.D. performed the of nonlinear optical signals are detected by a spectrometer (Andor, experiments with assistance from Y.W., S.D., H.X., X.B., and Hamamatsu) in the reflection configuration. The nonlinear optical E.H. on the device fabrication and characterization. G.Z., X.Y., signals of monolayer MoS were measured under different gate and Q.D. provided the CVD-grown MoS sample. Y.D. voltages. Note that when different source−drain voltages were applied, no change was observed in nonlinear optical signals. analyzed the experimental data. Y.D. and Z.S. wrote the Therefore, to fully exclude the electric-current-induced nonlinear manuscript with contributions from all authors. optical effects (e.g., current-induced second-order nonlinearity ), we Notes only apply gate-voltage and ground source and drain electrodes (i.e., The authors declare no competing financial interest. no source−drain current) in our experiments. ACKNOWLEDGMENTS ASSOCIATED CONTENT We acknowledge funding from the Aalto Centre for Quantum sı * Supporting Information Engineering, Business Finland (A-Photonics), Academy of The Supporting Information is available free of charge at Finland (grant nos. 276376, 284548, 295777, 304666, 312297, https://pubs.acs.org/doi/10.1021/acsnano.0c02642. 312551, and 314810), Academy of Finland Flagship Programme (grant no. 320167, PREIN), the European Union’s MoS film characterization, gate-tunable electrical and Horizon 2020 research and innovation program (Grant No. linear optical properties of monolayer MoS , FWM and 820423, S2QUIP), and ERC (grant no. 834742). SFG experiment setup and spectra of pump light, nonlinear optical spectra in monolayer MoS ,the REFERENCES repeatable gate-tunable FWM, gate-tunable SFG spectra (1) Manzeli, S.; Ovchinnikov, D.; Pasquier, D.; Yazyev, O. V.; Kis, A. with excitonic resonance and off-resonance, calculation 2D Transition Metal Dichalcogenides. Nat. Rev. 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Published: Jun 29, 2020

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