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Masaki Tanabe, Ritsuki Okukawa, Tomoyuki Yokouchi, [Yasumitsu Miyata](https://orcid.org/0000-0002-9733-5119), Yuki Shiomi

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This is the Accepted Manuscript version of an article accepted for publication in Japanese Journal of Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://doi.org/10.35848/1347-4065/add5b2.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Pockels effect in CVD-grown monolayer MoS<sub>2</sub>](https://mdr.nims.go.jp/datasets/4d28c820-42f2-4cd4-837b-5c9b50647561)

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Pockels effect in CVD-grown monolayer MoS2Masaki Tanabe1, Ritsuki Okukawa2, Tomoyuki Yokouchi3, YasumitsuMiyata2,4, and Yuki Shiomi11 Department of Basic Science, The University of Tokyo, Tokyo 153-8902, Japan2 Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan3 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan4 Research Center for Materials Nanoarchitectonics, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapanE-mail: yukishiomi@g.ecc.u-tokyo.ac.jpAbstract. We have studied the Pockels effect, that is, the linear change in the refractive indexof piezoelectric materials in response to an electric field, in monolayer and bilayer MoS2 filmsgrown by a chemical vapor deposition method. Optical imaging of the polarization rotation ofthe reflected light reveals that the polarization plane rotates by the application of an electricfield only in monolayer MoS2 which lacks inversion symmetry. The Pockels coefficient r22is estimated to be −1.4 pm/V for monolayer MoS2, which is comparable to the magnitudereported for GaAs.1. IntroductionSince the groundbreaking work on graphene in 2004 [1], two-dimensional (2D) materialshave been the focus of significant research efforts. 2D materials can be easily separated fromadjacent layers that are weakly bonded by van der Waals forces, and atomically thin samplescan be readily obtained just using adhesive tapes. Mechanical exfoliation is very simple, andthe products are of high quality. However, each flake has a different number of layers that arerandomly dispersed on the substrate, and the size is often small. Hence, various approacheshave been developed for the preparation of 2D materials. One useful method is chemicalvapor deposition (CVD), which enables the growth of large-scale 2D materials on varioussubstrates [2, 3]. In addition to the tremendous number of material species in 2D materials[4], different atomically thin 2D materials can be stacked together by van der Waals forces toform 2D heterostructures. These atomic-layer 2D materials and 2D heterostructures display arich variety of physical properties, which are promising for diverse applications [5, 6] such aselectronics, photonics, optomechanics, and spintronics.Besides graphene, widely studied are the family of transition metal dichalcogenides(TMDs) of the type MX2, where M is a transition metal atom (Mo, W, etc.) and X is achalcogen atom (S, Se, or Te) [7]. Unlike graphene which has no band gap, most TMDsare semiconductors that are ideal for electronic and photonic applications. The most well-known representative of TMDs is MoS2. MoS2 is a hexagonal crystal with layered structuresPockels effect in CVD-grown monolayer MoS2 2stacked by alternating S-Mo-S layers. In the bulk, MoS2 is a semiconductor with an indirectband gap of ∼1.2 eV, but monolayer MoS2 presents a direct band gap owing to quantumconfinement [8, 9]. The direct band gap is suitable for efficient light applications, suchas optoelectronics and nanophotonics. For example, ultrasensitive photodetectors based onMoS2 have been developed [10]. TMDs are now considered important optical materials,since they are compatible with Si-based photonic devices and also provide additional value,e.g. mechanical flexibility, easy fabrication and integration, and robustness [11, 12].The stacking degrees of freedom are another important property that modulates thephysical properties of 2D materials. As to MoS2, the electronic properties are largely modifiedby the number of layers and their stacking arrangement [13] because of variations in electronicand interlayer couplings. For example, the band gap in MoS2 bilayer is altered by stackingas well as by several other means, such as strain [14, 15], sliding [16], and twisting [17].Another important aspect of multilayers is the manipulation of symmetry breaking throughstacking. This offers the possibility of manipulating the internal quantum degrees of freedom,such as spin, valley, and layer pseudospin in 2D materials, giving rise to exotic phenomena inspintronics, valleytronics, and twistronics [18]. Gate control of symmetry breaking was alsodemonstrated in bilayer MoS2 [19, 20].Symmetry breaking in materials is also essential in nonlinear optics which has developedinto a key technology in condensed-matter physics, light generation, and quantum optics[21]. Nonlinear optical processes emerge from higher order expansion terms of polarization.Second-harmonic generation, sum- and difference frequency generation, optic rectification,and the Pockels effect are described by second-order nonlinear optical effects that are allowedin noncentrosymmetric crystals [22]. In the Pockels effect (or linear electro-optic effect),the application of a static electric field changes the refractive index of the materials. ThePockels effect can only occur in a material that lacks the center of inversion symmetry, and isthereby forbidden in centrosymmetric materials, except at their surfaces with broken inversionsymmetry. Electro-optic modulation based on the Pockels effect which provides femto- orattoseconds response times [23] is one of the most fundamental applications of nonlinearoptical materials, and serves a broad spectrum of applications, including telecommunications,quantum optics, optical computing, and biomedical imaging [24, 25, 26, 27, 28].Though commercial nonlinear media are mainly bulk noncentrosymmetric crystals,TMDs and other 2D materials with low symmetry are considered promising materials forminiaturizing photonic and optoelectronic devices for on-chip integration [29] . Since TMDswith an odd number of layers can lack inversion symmetry as demonstrated by piezoelectricmeasurements [30, 31], second-order nonlinear optical effects are allowed that are not presentin TMD crystals with an even number of layers. However, although the second-harmonicgeneration has been frequently used to characterize symmetry breaking [32], less attentionhas been paid to the Pockels effect in TMDs, to the best of our knowledge [11, 29, 33, 34].In the present work, we experimentally study the Pockels effect for monolayer MoS2 with abroken inversion symmetry at room temperature.Pockels effect in CVD-grown monolayer MoS2 32. Methods2.1. ExperimentsMonolayer and bilayer MoS2 lateral junctions were prepared on Si/SiO2 substrates using asalt-assisted CVD method, as described previously [35]. For CVD growth, MoO2 powdersand S flakes were used as precursors and KBr powders were used as growth promoters.An optical image of the grown samples is shown in Fig. 1(a). Monolayer MoS2 singlecrystals were grown in triangular shapes with lateral sizes over 30 µm. Triangular MoS2bilayer domains were found in the central part of the monolayer MoS2. We obtainedbilayer domains where MoS2 triangles are stacked so that the vertices of each layer facein opposite directions, indicating a 2H-stacking configuration [36]. Since the 2H-stackedbilayer preserves the space inversion symmetry, the Pockels effect is forbidden for the bilayerdomains, whereas it is allowed in the monolayer region lacking inversion symmetry. In/Auelectrodes were fabricated on selected MoS2 grains using maskless photolithography andresistive evaporation, as shown in Figs. 1(a) and (b).Figure 1(c) shows the Raman spectra of monolayer and bilayer crystals excited by a532 nm line in air ambient environment (LabRAM HR Evolution equipped with an EMCCDcamera (HORIBA Scientific)). E2g (∼ 386-387 cm−1) and A1g (∼ 406-407 cm−1) modeswere observed in both domains. For the bilayer domain, the frequency of E2g peak decreases,whereas that of the A1g peak increases from that of the monolayer domain. This thicknessdependence is well consistent with the previous reports [37, 38].To measure the Pockels effect, we used an optical system similar to the setup used forthe polar magneto-optical Kerr effect [39, 40], which was constructed based on our previouspaper [41]. A schematic drawing of the system is shown in Fig. 2(a). Linearly polarized laserlight with a wavelength of 632.8 nm and power of 5 mW is focused at normal incidence ontothe MoS2 monolayer-bilayer crystals using a 100× microscope objective lens. The spot sizeis approximately 3 µm, and the position of the spot is scanned using an automatic stage toobtain a two-dimensional (2D) image. The reflected laser light is split by a Wollaston prismand detected by a balanced detector to analyze the polarization rotation. An ac electric fieldwith a frequency of 1.563 kHz was applied along an in-plane direction of the sample, andthe ac voltage signal from the balanced detector with the same frequency as that of the acelectric field was recorded using a lock-in amplifier. The polarization of the incident laserlight is fixed in the electric-field direction. All the measurements were performed at roomtemperature. Gate voltage was not applied to MoS2 in our measurements. The shift of thephotoluminescence peak to a lower energy (∼ 1.8 eV) (not shown) suggests that the MoS2crystals are clamped onto Si/SiO2 substrates [42].2.2. Analytical ModelHereafter, the principal dielectric axes x1, x2, and x3 in Fig. 1(b) are also denoted as x, y,and z, respectively. Owing to the Pockels effect, the refractive indices (second-rank tensor) ni(i = 1-6) in low-symmetry semiconductors change from the principal refractive indices uponPockels effect in CVD-grown monolayer MoS2 4(b)bilayermonolayerIn/Au// EMoS(a)Ew360 400 4402LRamanIntensityRaman Shift (cm-1)E2g A1g1L(arb.units)(c)10mm100mmFigure 1. Monolayer and bilayer MoS2 single crystals. (a) CVD-grown MoS2 samples.Electrodes were fabricated for the selected samples. (b) Left: Optical image of a monolayer-bilayer MoS2 film. The distance between the electrodes is set to 20-25 µm. Right: Crystalstructure of MoS2. x1, x2, and x3 denote principal dielectric axes. Electric field (E) is appliedalmost parallel to the x1 axis. Eω denotes the polarization direction of the incident light. (c)Raman spectra of monolayer (1L) and bilayer (2L) MoS2 domains. The black data representbackground signals obtained from the substrate.the application of the electric field E j ( j = 1-3). The Pockels effect is generally written as[43]∆(1ni)2=3∑j=1ri jE j. (1)Here, the change in the inverse permittivity tensor ∆(1/n2i ) is expanded by the electric field,and the first order term of the electric field is the Pockels effect. ri j are the Pockels coefficientsand represented as a 6×3 matrix. Since the even-layer MoS2 is centrosymmetric (point groupof 6/mmm), all ri j elements are zero. By contrast, the inversion symmetry of the odd-layerMoS2 (6̄m2) is broken, and r12, r22, and r61 can be nonzero. When we apply electric field Ealong the x1 axis of MoS2 [Fig. 1(b)], the change in the refrative index reads∆(1n6)2= r61E =−2r22E. (2)For symmetry of 6̄m2, r12 =−r22 and r61 =−2r22 are expected.The refractive index ellipsoid is then expressed asx2 + y2n20+z2n23−4r22Exy = 1. (3)Here we used n1 = n2 = n0 in the MoS2 layer. When we use a new, rotated coordinatex′ =x− y√2, y′ =x+ y√2, z′ = z, (4)Pockels effect in CVD-grown monolayer MoS2 5the index ellipsoid becomes(1n20−2r22E)x′2 +(1n20+2r22E)y′2 +z2n23= 1. (5)The x′ and y′ axes are the coordinate system rotated −π/4 around the z axis from the originalx and y coordinate axes. Note that x′, y′, and z are the principal dielectric axes under an electricfield applied along the x axis. The refractive indices modulated by the Pockels effect readnx′ = n0 +n30r22E ≡ n0 +∆n (6)ny′ = n0 −n30r22E ≡ n0 −∆n (7)nz = n3. (8)In our experiment, the laser light with the linear polarization along the x (x1) axis isirradiated from the z (x3) axis. The electric-field dependence of nx′ and ny′ changes the linearpolarization of the incident light to elliptical polarization, and also gives rise to the rotationof the polarization of the light. The oscillating electric field of the incident laser light isexpressed in the (x′, y′) coordinate asEi = (acos(ωt − kz), acos(ωt − kz)). (9)a, ω , t, and k are the amplitude, angular frequency, time, and wavenumber, respectively. Dueto the Pockels effect, the amplitude and phase of the reflected light change from those of theincident light:Er = (Ex′, Ey′) = (ax′ cos(ωt − kz+δx′), ay′ cos(ωt − kz+δy′)), (10)where ax′ ̸= ay′ and δx′ ̸= δy′ . Then we obtain(Ex′ax′)2+(Ey′ay′)2−2Ex′ax′Ey′ay′cos(δy′ −δx′) = sin2(δy′ −δx′). (11)Hence, the reflected light has elliptical polarization. This equation can be transformed tothe standard form equation of an ellipse in the α-rotated coordinate system from the (x′,y′)coordinate. α is determined bytan2α =2ax′ay′ cos(δy′ −δx′)a2x′ −a2y′. (12)When the modulation of the amplitudes due to the Pockels effect is small, i.e. ax′, ay′ ≈ a,then α ≈ π/4.According to the Fresnel equations, the amplitudes of the reflected light areax′ =(1−nx′1+nx′)a ≡ r⊥x′a, ay′ =(1−ny′1+ny′)a ≡ r⊥y′a. (13)Pockels effect in CVD-grown monolayer MoS2 6(a)HWPPolarizerHe-Ne LaserBSxyz stagesampleWollaston Balanced detectorPrismObjectivelensHigh passfilterInRef outRef inSignal outvoltage sourceLockinamp(b)Pd/GaAs0 50 10000.20.40.6Electric field (kV/m)Polarization rotation (mrad)Figure 2. Measurement setup and test results. (a) Schematic diagram of the measurementsetup for the polarization rotation due to the Pockels effect. HWP and BS denote the half-waveplate and the beam splitter, respectively. (b) Test results for the Pd/GaAs junction. Electric-field dependence of polarization rotation. The dotted line represents a linear fit.We assume that the polarization rotation due to the Pockels effect ∆α is small. Using theabove relations and α = π/4+∆α , we obtain∆α =14(r⊥y′r⊥x′− r⊥x′r⊥y′), (14)where δy′ −δx′ ≪ 1 and ∆α ≪ 1 were used. Using eqs.(6)-(8) and (13), ∆α is expressed as∆α =21−n20∆n =2n301−n20r22E. (15)Here we used ∆n ≪ 1. Therefore, the polarization rotation due to the Pockels effect isproportional to the change in the refractive index ∆n. n0 ≈ 3.7 was reported for monolayerMoS2 at 632.8 nm [44]. By measuring electric-field dependence of ∆α , the Pockelscoefficients can be estimated.Note that the effect of multiple reflections at different interfaces (e.g., Si/SiO2 interface)and the interference effects resulting from these multiple reflections have been reported to benontrivial [45]. Because the effects of multiple reflections were neglected in the magneto-optic Kerr effect measurement for monolayer CrI3 [46], we have simplified the analyticalmodel to a single reflection at the material interface.3. Results and DiscussionFirst, we performed test measurements on GaAs, a typical noncentrosymmetric semiconduc-tor. The point group of GaAs is 4̄3m, suggesting that r41 = r52 = r63(̸= 0) and all the otherPockels coefficients are zero. Also, initially nx = ny = nz = n0. When we apply the electricfield along the z axis, the Pockels effect is expressed as∆(1n6)2= r41E. (16)Pockels effect in CVD-grown monolayer MoS2 7 !"!! !"!! !"!! !"!!#$%&%'!#(#"#'!'"$ !)*+,-3 mrad-3 mrad(a) (b)[mm][mm]0 20 40 0 20 400204002040Figure 3. Polarization rotation due to the Pockels effect in monolayer and bilayer MoS2crystal. 2D mapping of (a) intensity of the reflected light and (b) polarization rotation forMoS2 monolayer-bilayer sample. The applied voltage was set to 20 V. The electrode distanceis 20 µm for this device.The refractive index ellipsoid then becomesx2 + y2 + z2n20+2r41Exy = 1. (17)By the same procedure as in the previous section, we obtainednx′ = n0 −12n30r41E (18)ny′ = n0 +12n30r41E (19)nz = n0. (20)These equations are similar to those in eqs.(6)-(8), and thus polarization rotation is alsoexpected in GaAs.The test sample is a commercially available undoped GaAs substrate with mirrorsurfaces. On the top surface that orients (001), thin Pd films were deposited at roomtemperature using a compact sputtering coater to apply an electric field to the metal/GaAsinterface. The electrode distance is 450 µm. The laser light was irradiated from the [001]axis.Figure 2(b) shows the electric-field dependence of the polarization rotation for Pd/GaAs.Polarization rotation was prominent around the Pd/GaAs interface, indicating that the voltageis concentrated near the interface. The averaged data over the region in which the signalwas observed are plotted in Fig. 2(b). By linear fit in Fig. 2(b), we estimated ∆α/E to be5.4×10−12 rad m/V. Using n0 = 3.8 [47], we obtain r41 =−1.3 pm/V. This value is close tothe textbook value: −1.17 pm/V [48]. We have thereby judged that our measurement systemprovides reliable data.We then measured the Pockels effect for the monolayer and bilayer MoS2 crystals.During the measurement, we faced several problems; for example, some samples crackedPockels effect in CVD-grown monolayer MoS2 85V 10V20V 2L1L(a) (b)30 mrad-30 mrad0 0 0.2 0.4 0.6 0.8 10510Electric field (MV/m)PolarizationRotation(mrad)Figure 4. Electric-field dependence of polarization rotation in monolayer (1L) and bilayer (2L)MoS2 crystal. (a) 2D mapping of the polarization rotation measured at different electric fields.(b) Electric-field dependence of the polarization rotation obtained from the experimental datashown in (a). The dotted line is a linear fit.near the central portion by the application of a large electric field (∼ 50 V). This is possiblyattributed to the inverse piezoelectric effect, where the generated stress could overcome thatfrom the substrate and produce strain. Nevertheless, we successfully observed a polarizationrotation in response to an electric field in a relatively small voltage range (≤ 20 V) for severalMoS2 samples, as shown in Fig. 3.Figure 3 shows a 2D mapping of the intensity of the reflected laser light [Fig. 3(a)] andpolarization rotation [Fig. 3(b)] measured at 1 MV/m for a monolayer-bilayer MoS2 sample.As shown in Fig. 3(b), we observed polarization rotation in the entire monolayer area. In thismeasurement, the polarization rotation was approximately 3 µrad. Remarkably, the signal isless pronounced in the bilayer region; the polarization rotation is almost zero, as shown inFig. 3(b). See Fig. 3(a) for the location of the bilayer domain. This result is consistent withthe symmetry condition of the second-order nonlinear optical effects. The Pockels effect isactive only in monolayer MoS2 which lacks the inversion symmetry.To estimate the Pockels coefficient in monolayer MoS2, we subsequently performedsystematic measurements under different electric fields, as shown in Fig. 4. Polarizationrotation due to the Pockels effect is reproduced in this measurement, and the signals wereobserved in the entire monolayer regime. As shown in Fig. 4(a), the polarization rotationbecomes larger monotonically with increasing electric field.The magnitude of the polarization rotation is averaged over the area where the signal isvisible, and plotted against the electric field in Fig. 4(b). An almost linear dependence isobserved, as expected. Using a linear fit, the slope corresponding to ∆α/E is estimated as1.1× 10−11 rad m/V. By using n0 ≈ 3.7 [44], eq.(15) yields r22 = −1.4 pm/V for the MoS2monolayer. Hence, the similar value of the Pockels coefficient to GaAs is obtained.The Pockels effect for the MoS2 monolayer was theoretically studied by M. Balaei etal. [49], and the second order of electrical conductivity related to the Pockels effect wascalculated. From the real part of the permittivity calculated from the conductivity results, wehave estimated ∆n. Then, we roughly obtain a Pockels coefficient to be −0.8 pm/V. Here, wePockels effect in CVD-grown monolayer MoS2 9assumed n0 ≈ 3.7 [44]. Our experimental results are thereby consistent with the theoreticallyestimated value.The Pockels coefficients of inorganic bulk semiconductors are typically in the range of1-10 pm/V [48]. For 2D materials, a first-principles calculation predicts that monolayer SnSexhibits a large Pockels effect with r31 = −50 pm/V [33]. Very recently, the Pockels effectwas experimentally studied in CuInP2S6 flakes [34]. The out-of-plane Pockels coefficientwas obtained as 20.28 pm/V. Compared with these results for other 2D materials, the Pockelscoefficient of monolayer MoS2 is not very large. However, our results show that the Pockelseffect occurs even in the monolayer limit of TMD, and its magnitude is still comparable to thetypical values reported for bulk crystals. These findings should be an important step towardthe application of TMDs in nanoscale photonic and optoelectronic devices.4. ConclusionIn summary, we experimentally demonstrated the Pockels effect for CVD-grown monolayerMoS2, which is one of the most important 2D semiconductors for various applications.The measurement system was validated for a typical semiconductor GaAs prior to themeasurements of MoS2. From the polarization rotation in response to the applied electricfield, the Pockels coefficient r22 was estimated as −1.4 pm/V for the MoS2 monolayer. Thisvalue is comparable to that of typical semiconductors e.g. GaAs and ZnS, and consistent withthe theoretically predicted value. The present results may constitute an important buildingblock for realizing on-chip nonlinear optical devices based on 2D materials [50].Based on these results, several important research directions are possible. First, thePockels effect is also expected in other odd-layer MoS2 crystals (three-layer, five-layer, etc.).It is therefore worthwhile to investigate the layer dependence of the Pockels effect. Becausethe second-order optical susceptibility decreases with increasing number of layers [51, 52], thePockels coefficient could be smaller for thicker samples. We note that the piezoelectric effectfor MoS2 shows a similar tendency; the piezoelectric coefficient for trilayer MoS2 samples isalmost half that for monolayer MoS2 [30].Second, because the refractive index of MoS2 depends on the wavelength of light,especially around the bandgap energy [53], future Pockels measurements for differentwavelengths are important. It is notable that the monolayer MoS2 bandgap was shown tobe controlled by the dielectric environment [54]. Tunable Pockels cells could be realizedusing the bandgap modulation property of MoS2 monolayer.AcknowledgmentsWe thank Mr. Shotaro Yotsuya and Prof. Daisuke Kiriya for the Raman measurement, Mr.Shota Toida for the device fabrication support, Mr. Takahiko Endo for the CVD growth, andProf. S. Fukatsu and Prof. S. Iguchi for the fruitful discussions. This work was supported bythe Japan Science and Technology Agency (JST) FOREST Program, Grant No. JPMJFR203Hand No. JPMJFR213X, and by the Japan Society for the Promotion of Science (JSPS)Pockels effect in CVD-grown monolayer MoS2 10KAKENHI, Grant No. JP21H05232, No. JP21H05234, No. JP22H04957, No. JP23K26525,No. JP24K21726, No. JP24H01177, and No. JP24K00566.References[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, andA. A. Firsov. 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