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Cheol-Yeon Cheon, Zhe Sun, Jiang Cao, Juan Francisco Gonzalez Marin, Mukesh Tripathi, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Mathieu Luisier, Andras Kis

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[Disorder-induced bulk photovoltaic effect in a centrosymmetric van der Waals material](https://mdr.nims.go.jp/datasets/cabd5085-406a-42a3-a6d4-86fed2e9c6df)

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Disorder-induced bulk photovoltaic effect in a centrosymmetric van der Waals materialARTICLE OPENDisorder-induced bulk photovoltaic effect in acentrosymmetric van der Waals materialCheol-Yeon Cheon1,2, Zhe Sun1,2, Jiang Cao3, Juan Francisco Gonzalez Marin 1,2, Mukesh Tripathi1,2, Kenji Watanabe 4,Takashi Taniguchi 5, Mathieu Luisier 3 and Andras Kis1,2✉Sunlight is widely seen as one of the most abundant forms of renewable energy, with photovoltaic cells based on pn junctionsbeing the most commonly used platform attempting to harness it. Unlike in conventional photovoltaic cells, the bulk photovoltaiceffect (BPVE) allows for the generation of photocurrent and photovoltage in a single material without the need to engineer a pnjunction and create a built-in electric field, thus offering a solution that can potentially exceed the Shockley–Queisser efficiencylimit. However, it requires a material with no inversion symmetry and is therefore absent in centrosymmetric materials. Here, wedemonstrate that breaking the inversion symmetry by structural disorder can induce BPVE in ultrathin PtSe2, a centrosymmetricsemiconducting van der Waals material. Homogenous illumination of defective PtSe2 by linearly and circularly polarized light resultsin a photoresponse termed as linear photogalvanic effect (LPGE) and circular photogalvanic effect (CPGE), which is mostly absent inthe pristine crystal. First-principles calculations reveal that LPGE originates from Se vacancies that act as asymmetric scatteringcenters for the photo-generated electron-hole pairs. Our work emphasizes the importance of defects to induce photovoltaicfunctionality in centrosymmetric materials and shows how the range of materials suitable for light sensing and energy-harvestingapplications can be extended.npj 2D Materials and Applications            (2023) 7:74 ; https://doi.org/10.1038/s41699-023-00435-8INTRODUCTIONExposing a crystal lacking inversion symmetry to light can result ina generation of photocurrent even at a zero-bias voltage due tothe so-called bulk photovoltaic effect (BPVE)1, a second-orderlight-matter interaction. Compared to the conventional photo-voltaic effect, which relies on the built-in electric field occurring atthe interface between two different materials, BPVE occurs in asingle material where photo-excited carriers are separated in real/momentum space due to the innate properties of the wavefunc-tion geometry2. BPVE is an attractive mechanism for harvestinglight energy because it is not restricted by the Shockley–Queisserefficiency limit3, and it has the potential to reach high conversionefficiencies in low-dimensional materials4. Nevertheless, thesefeatures of BPVE only apply to non-centrosymmetric materials,while centrosymmetric materials are devoid of BPVE due to therequirement of having a broken inversion symmetry1.The modification of the crystal structure with external meanscan overcome this restriction and allow for the manifestation ofBPVE in centrosymmetric materials by breaking the inversionsymmetry5. This approach has so far been applied to van derWaals (vdW) layered semiconductors, externally activating BPVEvia the use of a large strain gradient6, strain-induced polarization7,and reduced dimensionality8, enabled by their favorable mechan-ical properties. Despite the high BPVE coefficients of vdWmaterials achieved through this strain engineering6,7, device-related applications are limited by the need to form a hybridstructure with edges to exert local forces on the target material,which is prone to crack formation6. Alternatively, applying externalelectric fields is an effective way to break the inversion symmetryand realize BPVE9,10, but this requires large electric fields and ionicliquid gating, limiting the usefulness of this approach in practicalapplications.One practical way of breaking the inversion symmetry is byintroducing structural disorder. In two-dimensional (2D) materials,the most common form of structural disorder consists of pointdefects, giving rise to trap states for excited carriers11. Defects canalso locally break the inversion symmetry, allowing for second-order harmonic generation (SHG) in centrosymmetric materials12.Yet, there is no clear experimental proof that BPVE, despite beingthe DC counterpart of SHG, can be similarly induced by structuraldisorder in centrosymmetric materials. Such a finding would beimportant since it would not only broaden the number ofmaterials interesting for photovoltaic applications through defectengineering but also allow BPVE in a much simpler device schemethan the ones utilizing the mechanical deformation.RESULTSPtSe2, a vdW layered material, is a suitable testbed for the proof-of-principle investigation of disorder-induced BPVE because of itsinversion symmetry and its semiconducting nature in the few-layer form with a bandgap of 1.2 eV (0.4 eV) for the monolayer(bilayer) thickness13. The pristine PtSe2 crystal unit cell (Fig. 1a) ischaracterized by an octahedral coordination of Se atoms aroundPt with a trigonal (T) unit cell. A PtSe2 monolayer (1 L) consists ofone Pt layer sandwiched between two Se layers. The inversionsymmetry of PtSe2 is preserved from monolayer to its bulk formdue to AA vdW stacking (Fig. 1b). Its structure belongs to thecentrosymmetric space group of P3m1, with Se and Pt sitesbelonging to polar point groups C3v and D3d, respectively. Recent1Electrical Engineering Institute, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. 2Institute of Materials Science and Engineering, ÉcolePolytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. 3Integrated Systems Laboratory, ETH Zürich, 8092 Zurich, Switzerland. 4Research Center forFunctional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5International Center for Materials Nanoarchitectonics, National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. ✉email: andras.kis@epfl.chwww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00435-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00435-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00435-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00435-8&domain=pdfhttp://orcid.org/0000-0001-5648-7493http://orcid.org/0000-0001-5648-7493http://orcid.org/0000-0001-5648-7493http://orcid.org/0000-0001-5648-7493http://orcid.org/0000-0001-5648-7493http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-2212-7972http://orcid.org/0000-0002-2212-7972http://orcid.org/0000-0002-2212-7972http://orcid.org/0000-0002-2212-7972http://orcid.org/0000-0002-2212-7972https://doi.org/10.1038/s41699-023-00435-8mailto:andras.kis@epfl.chwww.nature.com/npj2dmaterialsstudies suggest that point defects such as Se and Pt vacanciesplay an important role in PtSe2 to induce phenomena that areotherwise symmetry-forbidden in the pristine form, e.g., spin–orbitsplitting14,15 and Rashba interaction16. Here, along the line ofdefect-induced properties found in this material, we provideevidence of the emergence of BPVE in semiconducting 2D PtSe2due to the breaking of local inversion symmetry by structuraldisorder.Producing defective PtSe2 crystalsFor this study, ultrathin 2D PtSe2 was produced using regular tapeexfoliation (RE) and Au-assisted exfoliation (AE) technique, thelatter of which is a method suitable for obtaining ultrathin large-area crystals17 (see Methods for more details). The structuralquality of the produced crystals was first analyzed by Ramanspectroscopy, as shown in Fig. 1c. Although both AE and REsamples show characteristic Raman peaks due to Eg, A1g, andlongitudinal optical (LO) phonon modes18, the intensity of theprominent Eg peak, due to the intra-layer in-plane vibration modeof top and bottom Se atoms, is significantly reduced in AE samplewith respect to the RE sample. Also, compared to the RE sample,the Eg peak in the AE sample redshifts by ~1.5 cm−1 and shows atwo-fold broadening. The origin of these Raman features can beattributed to the higher concentration of defects in the AE sample,possibly related to VSe, in analogy to the redshift and broadeningobserved for the E’ mode of monolayer MoS2 with sulfurvacancies19. In Supplementary Note 1, we further compare theredshift and broadening of the Eg peak between AE and REsamples and show that their difference gradually decreases withthe number of layers with no noticeable difference for the bulksamples. This indicates that the structural defects are mostly likelyoccurring within the top few layers of AE PtSe2, which makes theRaman spectra of monolayer PtSe2 most sensitive to the presenceof defects. Such defect formation could be due to sputtering bythe incoming Au atoms during the deposition involved in the AEtechnique enabled by relatively low displacement thresholdvacancy creation energy for chalcogen defects in PtSe220,21. Tosupport the hypothesis that the AE sample is physically damaged,we have reproduced the general features of the Raman spectrumassociated with the AE sample by applying a mild plasmatreatment on the RE sample (see Supplementary Note 2). Usingaberration-corrected high-angle annular dark-field scanningtransmission electron microscopy (HAADF-STEM) imaging, wedirectly visualize and confirm the presence of defects in AE PtSe2(Fig. 1d, e). We can identify Se vacancies (VSe) as well as largecluster-like defects, both of which locally break the inversionsymmetry of the pristine PtSe2 lattice. Thus, in the later text, wedesignate the AE (RE) sample as structurally defective (pristine).Polarization-dependent spontaneous photoresponse indefective PtSe2To study the impact of defects on the photoresponse of PtSe2, wehave performed polarization-controlled scanning photovoltagemicroscopy (Fig. 2a). Furthermore, we compare the photovoltaicresponse from multi-terminal devices made of defective andpristine bilayer PtSe2 on a SiO2/Si substrate (Fig. 2b). Firstly, theopen-circuit voltage is simultaneously measured while scanningthe laser along the central line connecting the two probingelectrodes, with the profiles shown in Fig. 2c. The photovoltagefrom the pristine sample (Fig. 2c, bottom panel) is mainlycab160 170 180 190 200 210 220 230 240 2500.02.0x1044.0x1046.0x1048.0x1041.0x105Raman intensity(cnts)Raman shift(cm -1)EgA1g LORegular exf.Au-assised exf.(x10)PtSedetop viewside viewFig. 1 Defective PtSe2 crystal. a, b The unit cell (a) and top and side view of 1T-phase PtSe2 crystal structure (b). c Raman spectra ofmonolayer PtSe2 samples produced by regular exfoliation (black line) and Au-assisted exfoliation (red line). Dotted black lines indicatecharacteristic Raman peaks from the regular regular exfoliated sample that are related to Eg, A1g, and LO phonon modes of 1T-phase PtSe2.Raman intensity from the Au-assisted exfoliation sample is multiplied by a factor of 10 for comparison. d STEM-HAADF image of a bilayerPtSe2 from Au-assisted exfoliation. The cluster-like defects are highlighted by orange dashed circles. The scale bar is 2 nm. e STEM-HAADFimage with a small field of view. The green and gray dots represent Se and Pt atoms, respectively, and Se vacancies, displayed as dotted yellowcircles, are visible. The scale bar is 5 Å.C. Cheon et al.2npj 2D Materials and Applications (2023)    74 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;generated at the electrode/PtSe2 interface with the opposite signfrom the two interfaces, which can be attributed to thephotovoltaic effect in the Schottky diode formed at the contactand the photothermoelectric effect at the semiconductor/metaljunctions22,23. On the other hand, the interfacial photovoltaicresponse is relatively weak in the defective sample (Fig. 2c, toppanel). Instead, the photovoltage increases when laser illumina-tion occurs away from the electrodes and reaches its maximumwhen the spot is centered between the two electrodes, indicatingthat photovoltage is generated solely from defective PtSe2.Although both pristine and defective bilayer PtSe2 show gate-modulated source-drain current typical of semiconductors (seeSupplementary Note 3), we observe a significantly lower on/offcurrent ratio and linear I–V characteristics in the defective sample.These transport features indicate the metal-like character ofultrathin PtSe2 due to defect-induced mid-gap states24. This canad e fb cA ACDBMetal contacts0 45 90 135 180 225 270 315 360-15-10-5051015202530354045Photovoltage (�V)Photovoltage (�V)0 45 90 135 180 225 270 315 360-0.50.00.51.01.52.02.53.03.54.04.55.0-10-505101520253035Amplitude (μV)pristinedefectiveC L D1 D2D1x100PdObjectiveLinear polarizerQuarter-wave plateλ=647nmBDCDefective DefectivePristine Pristine0 2 4 6 8 10 12-40-2002040Photovoltage (μV)Distance (μm)0 2 4 6 8-40-2002040Photovoltage (μV)Distance (μm)VBilayer PtSe2Si substrateSiO2Quarter-wave plate angle (°) Quarter-wave plate angle (°)Fig. 2 Spatial and polarization-dependent photovoltaic response in defective bilayer PtSe2. a Schematic of the setup for scanningphotovoltage microscopy on a bilayer PtSe2 device. The optical excitation (λ= 647 nm, P= 200 µW) is focused using a 50× objective, resultingin a laser spot area of ~0.7 µm2. The optical helicity is controlled by rotating the optical axis of a quarter-wave plate with an angle of θ withrespect to the incident linear polarization direction (black line). b Optical micrographs of defective (top) and pristine (bottom) devices. Thescale bars are 5 µm. c Photovoltage line scans from defective (top panel) and pristine (bottom panel) devices between the two measuringelectrodes, along the dashed lines in b. d–e Photovoltage (black dots) as a function of θ for defective (d) and pristine (e) bilayer PtSe2. Data isobtained while laser illumination is centered between two measuring electrodes. Fitting from Eq. (1) is shown as a solid red curve. Dashedcolor lines represent three major components in the modulation indicated in Eq. 1; D1θþ D2 (blue, dashed line), C sinð2θÞ (red, dashed curve),and L sinð4θþ δÞ (black, dashed curve). The state of the light polarization determined by the angle of the wave plate is labeled at the top ofthe graphs. f Amplitudes of fitting parameters C, L, D1, and D2 in Eq. 1, extracted from defective and pristine samples. D1 values, which areaccounted for experimental drift for both samples, are multiplied 100-fold.C. Cheon et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    74 also explain why photovoltage at the interface is not prominent inthe defective sample: the photovoltaic effect is negligible due to asmaller Schottky barrier height as a result of Fermi-level pinningand defect states25.To further investigate photovoltage generation under homo-genous illumination on PtSe2, we control the light helicity using aquarter-wave plate (QWP) and compare the simultaneouslymeasured photovoltage from the defective (Fig. 2d) and pristine(Fig. 2e) samples. We observe a much stronger photovoltagemodulation and offset from the defective sample. A phenomen-ological expression for the photovoltage (Vph) dependence on thepolarization angle θ can be written as:Vph ¼ L sin 4θþ δð Þ þ C sin 2θð Þ þ D1θþ D2 (1)Here, L and C refer to the amplitude of the photovoltagemodulated with 4θ and 2θ-periodicity, which depends on linearand circular polarizations, respectively. The phase shift δ is due tothe initial linear polarization set by the linear polarizer. D1accounts for the sample drift during data acquisition and D2 is apolarization-independent offset. Parameters L, C, D1, and D2 canbe extracted from data by fitting to Eq. (1). We find largeramplitudes for all the parameters in the defective sample (Fig. 2f),with the exception of D1 which accounts for sample drift. Weobserve that zero-bias photocurrent has an identical spatialdistribution and polarization dependence as the photovoltage(see Supplementary Note 4). This supports the interpretation thatboth current and voltage responses originate from the homo-genous illumination of PtSe2. The amplitudes of the linear andcircular photocurrents increase linearly with the optical power,confirming the origin of the second-order response to the lightelectric field (see Supplementary Note 5).The photon-drag effect (PDE) is an alternative nonlinear effectthat can generate a similar polarization response as BPVE in 2Dmaterials26,27. Since PDE requires a net in-plane photon momen-tum, it should be negligible in our measurement condition ofnormal incident light. Also, PDE alone cannot sufficiently describethe difference in photoresponse between defective and pristinePtSe2, as it can appear both in centrosymmetric and non-centrosymmetric materials. Yet, the requirement of brokeninversion symmetry for BPVE is consistent with the structuraldisorder found in previous TEM and Raman analyses, making BPVEthe most favorable explanation for our experimental data.One possible explanation for BPVE induced by circularlypolarized excitation, termed circular photogalvanic effect (CPGE),is Rashba-type splitting in the band structure caused by structuraldefects. As for pristine 1T-phase PtSe2, the bands are spin-degenerate because of the structural inversion symmetry. In thecase of broken inversion symmetry, spin–orbit coupling can leadto spin-split bands in k-space with helical spin texture, the effect ofwhich is called Rashba-type splitting. It is worth noting that thedefect-induced Rashba effect was recently observed in bothmetallic and semiconducting PtSe2 from non-reciprocal chargetransport16. Another phenomenon that is directly related to suchsplitting is the CPGE9,28. It can be attributed to the fact that thespin-split bands have different optical selection rules for left- andright-handed excitation, and for the opposite light helicity, photo-excited charge carriers flow reversely in these split bands. As aresult, photocurrent changes its sign with light helicity.For materials with high symmetry, including 1T-PtSe2 (D3d) and3R-stacked transition metal dichalcogenides (C3v), CPGE shouldvanish at normal incidence due to symmetry-related arguments.Yet, it can occur if the symmetry of the material is reduced to asingle mirror symmetry or even further26, which is expected in thepresence of disorder. For defective PtSe2, the Se vacancy has C3vsymmetry, whereas the symmetry of cluster-like defects shown inFig. 1d can be the lowest C1 symmetry without a single mirrorsymmetry. Therefore, Rashba-type splitting induced by such low-symmetry defects is expected to be responsible for CPGE in PtSe2.In this study, however, we focus on elucidating the origin of BPVEinduced by linear polarization, which is the LPGE.First-principles calculationsFor that purpose, we apply an ab initio simulation approachcombining density functional theory (DFT), maximally localizedWannier functions (MLWF), and the non-equilibrium Green’sfunction (NEGF) formalism (see Methods for more details) toexplore light-matter interactions in bilayer PtSe2 with Se vacancies(Fig. 3a). Under linearly polarized illumination at a photonwavelength λph= 647 nm and zero built-in potential, the photo-current flowing through the defective structure is at least oneorder of magnitude larger than in the pristine case (Fig. 3b). Theoverall photo-excited current is then decomposed into its electronand hole components that are plotted along a line connecting thedevice electrodes (Fig. 3c). In the pristine case, the electron andhole currents exactly compensate each other at every location. Thiselectron–hole symmetry is broken by the presence of VSe wherethe behavior of the hole current is more affected by scattering atthe defect site than the electron one. This imbalance leads to a netnon-zero photocurrent similar to what is observed in experiments.The electron–hole asymmetry can be explained by inspectingthe band structures of pristine and defective PtSe2 bilayers, ascalculated with DFT (Fig. 3d). It is found that the valence band (VB)is more altered by the presence of VSe than the conduction band,with a downshift of the top VB by 40meV, compared to thepristine case. Consequently, the VSe creates local energy barriersthat are important for holes and almost negligible for electrons.The reflection of holes against these potential barriers breaks thesymmetry between the electron and hole currents, which inducesa net current flow (Fig. 3e). Interestingly when incident electricfield polarization is varied between 0° and 360° against VSe, thereflection coefficient of both holes and electrons exhibits aperiodic behavior with a period of 120° (Fig. 3f). The reflectioncoefficient of holes is effectively higher than that of electrons,which in turn leads to the net flow of photocurrent being highlyanisotropic (see Supplementary Note 6). This indicates that the VSebehaves as a triangular scattering center whose properties can bedescribed by a model based on a wedge-shaped potential lackingcentral symmetry29. Applied in various 2D systems for LPGE30–32,such a model commonly assumes that charged carriers, directedby alternating electric fields, are scattered by randomly locatedbut identically orientated triangular wedges. If we picture thesewedges to be at the position of each VSe (Fig. 4a) that arerandomly located, the scattering edges of each wedge are wellaligned with one another since the PtSe2 crystal lattice maintainsits 3-fold symmetry around VSe as seen from the previously shownSTEM image (Fig. 1e). Thus, VSe meets the criteria to be thesuitable atomic site for the wedges.Determining PtSe2 crystallographic direction from LPGEUnlike for CPGE, there is no restriction for a trigonal symmetryprohibiting LPGE under normal incidence32,33. This motivates us toderive a phenomenological equation of LPGE with the second-order susceptibility based on the C3v symmetry of VSe34, takinginto account the experimental conditions, the position of probingelectrodes, and the electric field of light, with respect to thecrystallographic direction of PtSe2 with VSe (see SupplementaryNote 7 for the derivation). The normalized photovoltage fromLPGE can be expressed asVLPGE ¼ sin 2 α� 32φþ 12κ� �(2)Here, α, φ, and κ are the electric field angle, the angle of thezig–zag direction of PtSe2, and the angle of the probing electrode,C. Cheon et al.4npj 2D Materials and Applications (2023)    74 Published in partnership with FCT NOVA with the support of E-MRSrespectively, with reference to the linear polarization direction setby the initial alignment of the fast axes of the linear polarizer andthe half-wave plate before its rotation. Since the LPGE phase in Eq.(2) is related to the zig–zag direction of PtSe2, we attempt toexperimentally determine its crystallographic orientation tosupport our main argument that VSe is the source of LPGE inPtSe2. We, therefore, realize a device with an array of electrodesplaced along the edge of PtSe2 (Fig. 4b). We investigate thephotovoltaic response measured from the diagonal pairs ofelectrodes while focusing the laser spot at the center of the PtSe2flake and controlling its linear polarization (Fig. 4c). Thephotovoltage measured from each of the diagonal pairs is plottedas a function of the linear polarization angle (Fig. 4d). Data arenormalized to visualize the continuous 30 degrees phase shiftsintroduced by sequentially measuring between diagonal pairs ofelectrodes in anti-clockwise order (in order of curves from top tobottom). Based on the 12 κ phase term in Eq. (2), the continuous 30°phase shift in Fig. 4d merely reflects the relative angle betweenneighboring electrodes, which is 60° and suggests φ to be a fixedvalue. Assuming an arbitrary φ when fitting each LPGE data withEq. (2) produces a set of electrode angles showing the 6-foldsymmetry of circularly oriented electrodes introduced by design(see Supplementary Note 8). By determining the electrode anglesof the device from the reflection mapping (see SupplementaryNote 9), we found from the fitting an average value φ= 43.7°(Fig. 4e).The exfoliated layered materials commonly show sharp edgeswhich belong to certain crystallographic orientations, the ten-dency of which is particularly strong for 1T-phase AA-stackedmaterials such as 1T-PtS235, with their cleaved edges belonging toone of three zig–zag directions. We find that this is also the casefor PtSe2, for which we find edges with a relative angle of 60°between electrodes #4 and #5, confirmed by AFM (Fig. 4f) andoptical microscopy imaging (the inset of Fig. 4f). There is onlyaround 5° difference between the angle of the sample edges andextracted zig-zag directions. Such a close match between opticallyidentified and electrically extracted edge directions providesstrong evidence that LPGE is induced by VSe in PtSe2 and suggests-0.5 0 0.5kxkx-1-0.8-0.6-0.4-0.200.20.40.60.81Energy(eV)-0.5 0 0.50.150.20.250.30.350.4-0.5 0 0.5-0.4-0.3-0.2-0.100.1Se vacancy40nmx-polarizedyxEnergy(eV)Energy(eV) CB edgeVB edge+Ti-Ri-i+Ri(2x)-Ti(2x)+i+i-i+i-i+i-i+ibd efca:electron :hole0 10 20 30 40-20246pristinedefectivePhotocurrent(A/m)Distance(nm)0 10 20 30 40-60-40-200204060Photocurrent(A/m)Distance(nm)electron(pris.)hole(pris.)electron(def.)hole(def.)electrodeelectrode10xdefect states0 60 120 180 240 300 3600.20.40.60.8Reflectionratio(arb.)Electric field angle (deg.) holeelectronnet current : +RiFig. 3 Ab initio simulation of photocurrent in defective PtSe2 bilayers from linear polarized light. a Simulated PtSe2 bilayer structure witha single Se vacancy introduced in the upper most Se layer. Linearly polarized light is shined over the entire structure. Here, the x-axis, whichconnects both device’s electrodes, is parallel to the armchair direction of PtSe2. b, c Spatial distribution of the photocurrent generated alongthe x-direction (b) and its electron and hole components (c) in pristine (empty circle) and defective (filled circle) PtSe2 with zero built-inpotential. d Band structure of pristine (red) and defective (blue) bilayer PtSe2. The magnified insets show the energy levels near theconduction (top inset) and valence (bottom inset) band edges. The 40meV bandshift of the top valence band edge is depicted as a greenarrow. e Proposed photocurrent generation model for defective PtSe2. Se vacancies act as scattering centers for the photo-generated holes,but not for electrons. It is assumed that each photo-generated carrier has the same current probability to flow toward +x and −x, i.e., ± i, sincethere is no applied electric field. For convenience, only three photo-generated electron–hole pairs are shown. Because of the inducedpotential barriers, holes have a probability R to be reflected against Se vacancies and T= 1− R to be transmitted. Hence, the electron and holecurrents become different (e.g., 3i for electrons and −(3− R)i for holes in the left electrode), giving rise to a net current flow of Ri in defectivePtSe2. f Electron and hole reflection probability as a function of their incident angle against the Se vacancies. 0 degree corresponds to carrierspropagating along the armchair direction of PtSe2.C. Cheon et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    74 the potential utility of LPGE for determining the crystal orientationof vdW crystals as an alternative to SHG.DISCUSSIONIn summary, our work has demonstrated BPVE induced bystructural disorder in a centrosymmetric material, PtSe2. We haveexamined defective semiconducting bilayer PtSe2 with Ramanspectroscopy and STEM, showing evidence of structural disorderintroduced by Au-assisted exfoliation. While pristine PtSe2 exhibitsa conventional photovoltaic response under zero-bias conditions,defective PtSe2 displays spontaneous photoresponse underhomogenous illumination and generates LPGE and CPGE. Weattribute the appearance of CPGE under normal incidence to thereduced crystal symmetry, possibly due to cluster-like defects inPtSe2. On the other hand, first-principle calculations capture ourexperimental findings on LPGE and suggest that Se vacancies actas asymmetric trigonal scattering sites to which photo-excitedelectrons and holes respond differently. Thus, disorder-inducedBPVE in PtSe2 is related to two types of defects that haveinherently different symmetries where the symmetry conditionsfor CPGE and LPGE are satisfied on a local scale. The wedgepotential model applied to the atomic site of Se vacancies allowedus to determine the crystallographic orientation of PtSe2experimentally. Our work extends the possible functionality ofdefects in centrosymmetric PtSe2 as a source for harvesting lightenergy and detecting light polarization and shows that defectengineering is a viable strategy for broadening the number ofpotentially interesting materials for BPVE-based photovoltaicapplications.METHODSAu-assisted exfoliationThe Au-assisted exfoliation was performed following the reportedprocedure17, which involves the evaporation of gold films on thebulk TMDC crystal. We first exfoliated bulk commercially availablePtSe2 (HQ graphene) on a blue dicing tape (Nitto). Then, weevaporated 100 nm-thick gold film using an electron beamevaporator. Using thermal release tape (Nitto 3195MS), we peeledoff the gold film, which would detach the topmost layers of bulkPtSe2, and transferred it to the SiO2/Si substrate at the releasingtemperature of 120 °C. The substrate was treated with mild O2plasma for 1 minute to remove the tape-related residue. The goldfilm was etched in an Au etchant, potassium iodide (KI), and iodine(I2) in DI water solution (1 g : 4 g : 40 g= I2: KI : H2O), for 5 minutesand then another 20 minutes in a new Au etchant solution. This isfollowed by a 5-min soaking in DI water to rinse away the Auetchant solution and a 30-min soaking in acetone and isopropanol(IPA) in order to remove any remaining polymer residues. As aresult, ultrathin PtSe2 samples were obtained with a larger areathan by the regular exfoliation method. The thickness of ultrathinPtSe2 was measured using atomic force microscopy (seeSupplementary Fig. S1). We note that we do not observe residualAu layers/atoms on PtSe2 after removing Au by Au etchant basedon EDX (see Supplementary Note 10).60°#4#5∆φ ~5°#1#2#3#4#5 #6ad e fb c1 2 3 4 5 60102030405060Zig-zagdirection(deg.)n-th diagonal pairφavg= 43.7��0.41�E: VSe : mirror planeTop h-BNPtSe2Top gateBottomh-BN Backgate#1#2#3#4#5 #623.5(nm)0.0VLinear polarizerHalf-wave plate-101-101-101-101-1010 60 120 180 240 300 360-101Electric field angle(deg.)Normalizedphotovolatge(a.u.)PtSe2-23.5V(#1)-V(#4)V(#2)-V(#5)V(#3)-V(#6)V(#4)-V(#1)V(#5)-V(#2)V(#6)-V(#3)φ2, ext.φ3, ext.Fig. 4 VSe-induced LPGE. a Top view of PtSe2 atomic structure with VSe (black circle). VSe has C3v symmetry with broken inversion symmetry. Agray triangle represents a triangular wedge. b The optical micrograph of h-BN encapsulated defective bilayer PtSe2 with circularly orientedelectrodes that are 60° apart. The optical micrograph of h-BN encapsulated defective bilayer PtSe2. The image is false-colored, highlightingdifferent materials, and the electrodes are numbered for clarity. The scale bar is 5 µm. c Schematic of the photovoltage measurement schemefrom diagonal electrode pairs. d Linear polarization-dependent photovoltage measured from six diagonal electrode pairs. LPGE responses arenormalized to emphasize the constant phase shift. e Extracted angles (φ) of the zig–zag direction from six diagonal pairs. f 2D height profileby AFM around the electrodes #4 and #5. Black lines are the edge of PtSe2 identified from AFM, which is 60° apart. Blue and red dash lines arethe extracted zig–zag directions. The scale bar is 1 µm. Inset is the optical micrograph of the same region of the device. The scale bar is 2 µm.C. Cheon et al.6npj 2D Materials and Applications (2023)    74 Published in partnership with FCT NOVA with the support of E-MRSRaman spectroscopyRaman spectroscopy measurement was performed at roomtemperature and atmospheric conditions using a confocalRenishaw inVia Confocal Raman microscope. A laser beam of532 nm wavelength with a power of 1 mW was focused by anobjective producing a Gaussian excitation area of 1 µm2 on targetsamples. To obtain high spectral resolution, 3000 lines/mmdiffraction grating was employed for the Raman spectra of PtSe2.Scanning transmission electron microscopySTEM imaging was performed using a Cs double aberration-corrected DCOR (CEOS) FEI Titan Themis. The Microscope isequipped with an X-FEG, Super-X EDX detector, and a Wein-typemonochromator. STEM imaging experiments were done using the80 kV primary acceleration voltage, probe convergence angle of20mrad, and the camera length was set to 185mm, whichcorresponds to the HAADF detector 49–200mrad collection angle.The estimated probe current was ~21 pA, and images wererecorded using 1024 × 1024 pixels and 6 µs dwell times. Thehigher-order aberrations were minimized using the tableau. Veloxsoftware, ThermoFisher Scientific, and double Gaussian filtering inImageJ were used to acquire and process the images. The positionof individual Pt and Se atoms is clearly discernible by the imagecontrast where the intensity is directly nth proportional to theatomic number (n= 1.64–2), depending on the detectorgeometry.Device fabricationDevice #1 (bilayer PtSe2 on Si/SiO2 substrate). The bilayer PtSe2was produced by the Au-assisted exfoliation method explainedabove. The samples were spin-coated with PMMA polymer andput on a hot plate at 180 °C for 5 min. Electron-beam lithographywas used to pattern the electrodes. Finally, an 80 nm Pd film wasdeposited by electron-beam evaporation for the electrodes,followed by a lift-off process using acetone to remove thePMMA layer.Device #2 (bilayer PtSe2 encapsulated with h-BN). The local metalgate (Cr 1 nm/Pt 5 nm) was fabricated using electron-beamlithography and electron-beam evaporation. Twenty-nanometrethick h-BN was used for the bottom gate dielectric. h-BN wasproduced by exfoliating it on a SiO2/Si substrate and thentransferred on the prepared local metal gate by van-der Waals(vdW) pick-up transfer method using a polycarbonate (PC) filmunder atmospheric exposure. PC film is released at 170 °C, and thefilm is cleaned with Chloroform for 6 hours and then withisopropyl alcohol, followed by high vacuum (below 10−5 mbar)annealing at 340 °C for 6 hours. After the cleaning, the pre-contactelectrodes (Pt 5 nm) were fabricated using electro-beam litho-graphy and electron-beam evaporation. Bilayer PtSe2, producedby Au-assisted exfoliation on a SiO2/Si substrate, was picked up by30 nm-thick top dielectric h-BN with PC film and released on thepre-contact electrodes with the same transferring and cleaningprotocol as bottom dielectric h-BN. Finally, the top local gate (Pt5 nm) and contact electrodes (Pd 80 nm) for the pre-contacts andlocal gates were fabricated using electro-beam lithography andelectron-beam evaporation.Optoelectronic measurementsScanning photocurrent and photovoltage microscopy was carriedout with focused light excitation. We used 647 nm wavelength asan excitation source above the energy of the bandgap (0.4 eV) ofbilayer PtSe2, which is focused into a Gaussian spot size (0.7 µm2)using a 50× objective while the excitation power was controlled bya neutral-density filter. As for the polarization control, the linearpolarizer is used to set the initial polarization direction, and aquarter-wave plate was used to produce circular polarizations. Itwas replaced by a half-wave plate in the case of controlling thedirection of linear polarization. Prior to rotating the wave plate, thefast axes of the linear polarizer and the wave plate are bothaligned. The objective was mounted on an XY nano-positioner tocontrol the excitation position on the sample, which was keptinside a high vacuum chamber (~10−5 mbar) during the measure-ment. The zero-biased photocurrent was measured by Keithley2450 sourcemeter with no external voltage applied between twocollecting electrodes. The photovoltage was measured in open-circuit conditions using an SR860 lock-in amplifier and amechanical chopper (freq. 723 Hz), where the data acquisitionwas averaged for 1 s at the time constant of 300ms. All the otherelectrodes in contact with PtSe2 not used for the electricalmeasurements were disconnected during the data acquisition.Ab initio simulationsThe DFT calculations were performed with VASP36 within thegeneralized gradient approximation of Perdew, Burke, andErnzerehof (PBE)37 using a Γ-centered Monkhorst–Pack k-pointgrid of dimension 21 × 21 × 1 and a plane-wave cutoff energy of550 eV. The DFT-D3 method of Grimme38 was adopted to accountfor the vdW interactions. The PtSe2 bilayer structure was relaxeduntil the forces acting on each ion became smaller than 10−4 eV/Å.The DFT results were then transformed into a set of MLWF withthe wannier90 code39. All the Wannier functions are well localizedwith a spread of less than 2.5 Å2. The MLWF Hamiltonian veryaccurately reproduces the DFT band structure. By applying anupscale technique on the hexagonal unit cell of the bilayer PtSe2,simulation domains of any size can be created, together with thecorresponding Hamiltonian matrix and momentum operator.Here, we restricted ourselves to a 40 nm long slab between twosemi-infinite leads that are treated as electrodes and collect thephoto-generated electrons and holes. All photocurrents weresimulated with a quantum transport solver relying on the NEGFformalism and dedicated electron–photon scattering self-energies(SSE) with ab initio inputs40. The electron-photon SSE can accountfor different polarization directions. Individual VSe’s were intro-duced by removing Se atoms from the top Se layer of the PtSe2bilayers. To separate the electron and hole contributions to thephotocurrent, we integrated the energy-resolved photo-excitedcurrent density within the energy range corresponding to theconduction and VBs, respectively. To map the directionaldependence of the electron/hole reflection probability at VSescattering sites, we calculated the contribution to the electron andhole photocurrents for different carrier momentum directions. Thereflection probability at VSe scattering sites was deduced from therelative difference between the photocurrents of pristine anddefective structures.DATA AVAILABILITYThe data that support the findings of this study are available from the correspondingauthor upon reasonable request.Received: 6 July 2023; Accepted: 17 October 2023;REFERENCES1. Sturman, B. I. & Fridkin, V. M. The Photovoltaic and Photorefractive Effects inNoncentrosymmetric Materials. (Routledge, 2021). https://doi.org/10.1201/9780203743416.2. Morimoto, T. & Nagaosa, N. Topological nature of nonlinear optical effects insolids. Sci. Adv. 2, e1501524 (2016).3. Spanier, J. E. et al. Power conversion efficiency exceeding the Shockley–Queisserlimit in a ferroelectric insulator. Nat. Photonics 10, 611–616 (2016).C. 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Devicefabrication was carried out at the EPFL Center for micro and nanotechnology.Electron microscopy imaging was performed at the EPFL Interdisciplinary Center forElectron Microscopy (CIME). This work was financially supported by the EuropeanResearch Council (grant 682332) and the Swiss National Science Foundation (grantsNos. 175822 and 164015). This work was financially supported by the EuropeanUnion’s Horizon 2020 research and innovation program under grant agreement No.881603 (Graphene Flagship Core 3). This research was also supported by the SwissNational Supercomputing Center (CSCS) under project s1119. J.C. and M.L. acknowl-edge support from the NCCR MARVEL, funded by the Swiss National ScienceFoundation (grant number 205602). K.W. and T.T. acknowledge support from JSPSKAKENHI (Grant Numbers 19H05790, 20H00354, and 21H05233).AUTHOR CONTRIBUTIONSA.K. initiated and supervised the work. C.-Y.C. performed material characterizationand device fabrication. C.-Y.C. performed the charge transport and optoelectronicmeasurements with initial assistance from Z.S. and J.M. for the optical setups. C.-Y.C.analyzed the optoelectronic data with input from A.K. and Z.S. M.T. conducted STEMmeasurements and analyzed the data. J.C. and M.L. performed the first-principlecalculations. K.W. and T.T. grew the h-BN crystals. C.-Y.C. and A.K. wrote themanuscript with input from all the authors.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-023-00435-8.Correspondence and requests for materials should be addressed to Andras Kis.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023C. Cheon et al.8npj 2D Materials and Applications (2023)    74 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41565-022-01252-8https://doi.org/10.1016/B978-0-12-811002-7.00010-2https://doi.org/10.1016/B978-0-12-811002-7.00010-2https://doi.org/10.1038/s41699-023-00435-8http://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Disorder-induced bulk photovoltaic effect in a centrosymmetric van der Waals material Introduction Results Producing defective PtSe2 crystals Polarization-dependent spontaneous photoresponse in defective PtSe2 First-principles calculations Determining PtSe2 crystallographic direction from�LPGE Discussion Methods Au-assisted exfoliation Raman spectroscopy Scanning transmission electron microscopy Device fabrication Device #1 (bilayer PtSe2 on Si/SiO2 substrate) Device #2 (bilayer PtSe2 encapsulated with�h-BN) Optoelectronic measurements Ab initio simulations DATA AVAILABILITY References Acknowledgements Author contributions Competing interests ADDITIONAL INFORMATION