Intense second-harmonic generation in two-dimensional PtSe 

: Platinum diselenide (PtSe 2 ), classiﬁed as a noble metal dichalcogenide, has garnered substantial interest owing to its layer-dependent band structure, remarkable air-stability, and high charge-carrier mobilities. These properties make it highly promising for a wide array of applications in next-generation electronic and optoelectronic devices, as well as sensors. Additionally, two-dimensional (2D) PtSe 2 demonstrates signiﬁcant potential as a saturable absorber due to its exceptional nonlinear optical response across an ultrabroad spectra range, presenting exciting opportunities in ultrafast and nonlinear photonics. In this work, we explore the second-order nonlinear optical characteristics of 2D PtSe 2 by analyzing its second-harmonic generation (SHG) excited by a pulsed laser at 1064 nm. Our investigation unveils a layer-dependent SHG response in PtSe 2 , with prominent SHG intensity observed in few-layer PtSe 2 . The distinct six-fold polarization dependence pattern observed in the SHG intensity reﬂects the inherent threefold rotational symmetry inherent to the PtSe 2 crystal structure. Remarkably, the SHG intensity of 4-layer PtSe 2 surpasses that of mechanically exfoliated monolayer molybdenum disulﬁde (MoS 2 ) by approximately two orders of magnitude (60-fold), underscoring its exceptional second-order non-linear optical response. Combined with its ultrahigh air-stability, these distinctive nonlinear optical characteristics


Introduction
Second-harmonic generation (SHG) in two-dimensional (2D) materials is an intriguing optical phenomenon where electrons are confined into a two-dimensional plane, leading to unique nonlinear optical behavior.When exposed to incident light, the electrons undergo oscillations, emitting light waves at twice the frequency through SHG process.This effect is particularly significant due to the exceptional electronic and optical properties of 2D materials, attracting considerable attention in nonlinear photonics and quantum technologies [1]- [6].The SHG process in 2D materials is intricately linked to their electronic structure and crystal symmetry [7].Materials with centrosymmetric properties typically lack SHG effects because their second-order nonlinear optical susceptibility is vanishing [8].Conversely, non-centrosymmetric 2D materials, like molybdenum disulfide (MoS 2 ) monolayer, exhibit strong SHG signals owing to its symmetry breaking [9]- [11].Strong SHG signal has also been observed in other 2D materials, like WS 2 [12], WSe 2 [13], ReS 2 [14], GaSe [15], [16], making these 2D materials attractive for the development of ultrathin nonlinear optical devices.
Manipulating external parameters, such as strain, electric field, incident light intensity, and polarization, offers precise control over SHG in 2D materials [17]- [23].For example, strain engineering can alter the lattice structure of graphene, inducing sublattice polarization to enhance SHG in monolayer graphene [17].External electric fields can induce strong, doping-induced SHG in centrosymmetric monolayer graphene, comparable in strength to SHG in non-centrosymmetric 2D materials [20].Additionally, electrostatic doping can tune the intensity of SHG at the Aexciton resonance of WSe 2 by over an order of magnitude at low temperatures and nearly fourfold at room temperature in a field-effect transistor [19].This level of control offers exciting prospects for applications, including highefficiency nonlinear devices and electrically tunable nonlinear optical devices for integrated quantum circuits.
Understanding the underlying principles which govern SHG in these materials is paramount for the design and development of novel devices with enhanced performance and functionality.By finely tailoring the characteristics of two-dimensional (2D) materials, it becomes possible to enhance and manipulate the efficiency of SHG and their nonlinear optical response [8], [24], [25].For instance, the chemical vapor deposition (CVD)-grown spiral tungsten disulfide (WS 2 ) nanosheets demonstrate a stronger SHG intensity that quadratically increases with their layer numbers due to the broken symmetry resulting from twisted screw structures [8].This phenomenon extends the potential applications of 2D materials in nonlinear optical technologies.The exploration of novel materials with distinct electronic or optical characteristics has led to the investigation of 2D materials exhibiting high-efficiency nonlinear optical responses for next-generation photonic technologies [3], [26], [27].One such material, layered niobium oxide dichloride (NbOCl 2 ), possesses vanishing interlayer electronic coupling and monolayer-like excitonic behavior even in bulk form.Notably, NbOCl 2 exhibits a scalable SHG intensity of up to three orders higher than that observed in conventional monolayer WS 2 , rendering it highly attractive for integration into nonlinear nanophotonic devices.Moreover, its strong second-order nonlinearity enables correlated parametric photon pair generation through a spontaneous parametric down-conversion (SPDC) process, even in flakes as thin as approximately 46 nm, establishing it as the thinnest SPDC source ever reported [3].
Beyond its potential applications in photonics, understanding the intricacies of SHG in 2D materials could lead to breakthroughs in materials science [28], [29] and fundamental physics [30].For instance, SHG in 2D materials is a highly sensitive probe of subtle magnetic orders, the observed giant nonreciprocal SHG revealing the layered antiferromagnetic order in chromium triiodide (CrI 3 ), opening up possibilities for the use of two-dimensional magnets in nonlinear and nonreciprocal optical devices, holding immense potential for unlocking unprecedented opportunities in next-generation photonic technologies [26], [31]; Insights gained from investigating SHG could also shed light on the underlying electronic structure and symmetry properties of 2D materials, advancing our knowledge of condensed matter physics [7], [29], [32], [33].
As representatives of 2D materials, graphene and conventional transition metal dichalcogenides like MoS 2 , MoSe 2 have captured considerable attention over the past decades [34]- [36].Beyond these established materials, a new class of layered materials has emerged, each offering unique functionalities.Among them, black phosphorus has gained prominence for its distinctive properties for its ultrahigh electron mobility [37], [38].Another notable 2D material is the class of noble metal dichalcogenides (NMDs) [39]- [43].Among them, compounds such as PtSe 2 and PdSe 2 have recently garnered significant interest owing to their remarkable characteristics.These materials exhibit exceptional environmental stability, outstanding electronic properties [41], [42], and giant optical nonlinearity [44].
Notably, layered PtSe 2 , with its capacity for lowtemperature synthesis, coupled with its high charge-carrier mobilities and enduring air stability, underscores its potential for electronic and optoelectronic applications [40], [45], [46].For instance, devices composed of a few layers of PtSe 2 demonstrate semiconducting behavior with impressive environmental resilience, showcasing a noteworthy roomtemperature electron mobility of 210 cm 2 V −1 s −1 when configured with a back gate on a SiO 2 /Si substrate [47].Furthermore, bilayer PtSe 2 , when combined with defect modulation, exhibits strong light absorption in the midinfrared region, enabling the realization of a broadband mid-infrared photoconductive detector [46].In addition, thin polycrystalline films of PtSe 2 , a centrosymmetric Dirac semimetal, exhibit giant photon momentum-locked terahertz (THz) emission, presenting exciting prospects for highly efficient THz signal activation [48].While the nonlinear optical absorption of layered PtSe 2 has been extensively studied [49], [50], its second-order optical nonlinearity remains unexplored.By measuring and analyzing the SHG signal of layered PtSe 2 , its second-order optical nonlinear properties could be further explored to uncover potential applications in nonlinear optics and beyond.
In this study, we explore the second-order optical nonlinearity of layered PtSe 2 through the characterization of its SHG excited by a pulsed laser operating at 1064 nm.The layered PtSe 2 samples are firstly prepared via goldassisted mechanical exfoliation, ensuring their high quality.The SHG measurements reveal that few-layer PtSe 2 exhibits a pronounced SHG intensity when pumped at 1064 nm.The inherent threefold rotation symmetry of the PtSe 2 crystal manifests in a distinct six-fold polarization dependence pattern observed in the SHG intensity.Notably, we observe a remarkable two-orders-of-magnitude enhancement (60fold) in the SHG intensity of 4-layer PtSe 2 compared to conventional monolayer MoS 2 , revealing the significant secondorder optical nonlinear response exhibited by 2D PtSe 2 .The strong SHG exhibited by 2D PtSe 2 , especially in the case of 4-layer PtSe 2 , positions 2D PtSe 2 as an attractive option for ultrathin and efficient nonlinear optical devices.In contrast to conventional transition metal dichalcogenides (TMDs), PtSe 2 demonstrates significantly stronger interlayer interactions, as evidenced by its calculated interlayer energy of 0.342 eV per unit cell [51].Consequently, the mechanical exfoliation of layered PtSe 2 flakes using conventional methods proves challenging.To address this, the developed gold-assisted mechanical exfoliation method [51]- [53] is employed to exfoliate a PtSe 2 single-crystal (purchased from 2D Semiconductors) into layered PtSe 2 flakes.

Results and discussion
In layered materials, the interaction between layers is primarily through van der Waals forces, while Au and many 2D materials including PtSe 2 can form covalent bonds.This interaction is stronger than van der Waals forces but weaker than covalent bonds, allowing for efficient exfoliation of large-area single-layer samples without affecting the intrinsic properties of the material.Initially, a Au (4 nm)/Ti (2 nm) thin film is deposited onto a silicon substrate at an evaporation rate of 0.5 Å/s via electron beam evaporation (utilizing the HHV Auto500).The 2 nm Ti layer served as an adhesion layer.Subsequently, the freshly cleaved layered bulk PtSe 2 crystal on tape is promptly brought into contact with the upper Au layer.Upon removal of the tape, the predominant portion of the crystal is extracted, leaving behind a few two-dimensional PtSe 2 layer flakes on the Au surface, successfully preparing the 2D layered PtSe 2 .
The optical microscope image of the fabricated layered PtSe 2 on the SiO 2 /Si substrate is captured using a microscope equipped with a CCD (ZEISS, Axiocam 208 color).The thickness of the layered PtSe 2 is characterized by an atomic force microscope (Bruker, BioScope Resolve).Figure 1(c  atomic-thin PtSe 2 flakes, while the yellow portions represent bulk material.The layer numbers could be characterized by the atomic force microscopy (AFM) measurements.AFM characterization of the thinner region within the box, as shown in Figure 1(d), reveals the atomic-thickness nature of the exfoliated flakes.The height profile along the white line denoted in Figure 1(d) confirms a thickness of approximately 1 nm, corresponding to bilayer PtSe 2 thickness with a single layer thickness of 0.5 nm (inset of Figure 1(d)).Furthermore, Raman spectra are acquired to further characterize the exfoliated PtSe 2 flakes, confirming the quality of the prepared sample (Figure S1).
Scanning transmission electron microscopy (STEM) images (measured by Thermo Scientific Spectra 300) and X-ray diffraction (XRD) patterns (obtained by Smartlab9KW) are employed to elucidate atomic structure and crystal quality of the prepared layered PtSe 2 .Figure 2(a) presents a cross-sectional STEM image of a thin PtSe 2 flake, revealing the distribution of Se and Pt atoms in the side view.The absence of obvious vacancies confirms the high quality of the PtSe 2 crystal.The observed layer pitch of approximately 0.5 nm aligns well with previous experimental findings (Figure 2(b)).
As shown in Figure 2(c), Analysis of selected area electron diffraction (SAED) patterns confirms the singlecrystalline nature of PtSe 2 , with a clear identification of the (001) crystal orientation.Furthermore, XRD analysis provides further insights into the crystal structure.The presence of four major characteristic peaks indicates the crystal's high quality, with other peaks likely suppressed due to the layered structure and specific (001) orientation of PtSe 2 (Figure 2(d)).Additionally, the presence of strong, narrow peaks corresponding to (001), ( 111), ( 202) and ( 113) lattice planes underscores the exceptional crystal quality of the fabricated samples [46], [54].
The SHG measurements are conducted using a microscope employing vertical reflection configuration.A pulsed laser, with a pulse width approximately 10 ps and a repetition rate around 20 MHz, emitting, at the central wavelength of 1064 nm, is precisely focused onto the sample at a normal angle of incidence through a 100× objective lens.The SHG signal, reflected from the sample, is gathered by the same objective lens and subsequently captured by a grating spectrometer fitted with a CCD camera.In the experiments, polarization-dependent SHG measurement is performed by placing a half-wave plate and analyzer in the incident and detection paths, respectively.In the parallel configuration, a step size of 10 • is used.Through SHG mappings, the layer-dependent SHG intensity could be clearly distinguished.The layer-dependent SHG intensity could be clearly distinguished by conducting SHG mappings with a laser spot size of 0.5 μm and high-resolution step size of 0.3 μm.The schematic diagram of the experimental setup can be found in Figure S2 in the Supplementary Material.
By comparing Figure 3(a) and (b), we observe a very weak SHG signal in monolayers.The lattice structures of 1Ttype PtSe 2 belongs to D 3d with preserved centrosymmetry and no intense SHG is expected to occur in layered PtSe 2 .Interestingly, intense SHG is observed for few-layer PtSe 2 .Similar phenomenon has been reported in 1T-type TiSe 2 and SnSe 2 [55], [56].One of its possible origins is the occurred lattice distortion associated with the charge density waves [56].Compared to bilayer PtSe 2 , we can observe a stronger signal in 4-layer PtSe 2 .Therefore, we further conducted SHG mapping tests on exfoliated few-layer PtSe 2 samples.As shown in Figure 3(c) and (d), we can see that the SHG signal intensity does not increase linearly with the number of layers.Instead, the strongest SHG signal intensity is observed in the 4-layer PtSe 2 sample.The SHG signal intensity of fewlayer PtSe 2 also varies with the number of layers due to the layer-dependent electronic structure and optical properties of PtSe 2 .No obvious SHG signal is detected in the bulk PtSe 2 .
In comparison to mechanically exfoliated monolayer MoS 2 , a well-known traditional strong SHG material [9], [10], the SHG intensity in 4-layer PtSe 2 excited by a 1064 nm wavelength laser is significantly higher by nearly two orders of magnitude (60-fold), as depicted in Figure 4   corresponding to the second-order nonlinear process, further confirming the emission of second-harmonic waves.The detailed layer-dependent SHG intensity is depicted in Figure 4(c).The 4-layer PtSe 2 with enhanced absorption demonstrates increased SHG, whereas with more than 4 layers, the stronger optical absorption in PtSe 2 impedes a higher SHG efficiency.Thus, the 4-layer PtSe 2 could serve as a potential candidate for 2D nonlinear optical applications.
Due to the in-plane lattice structure of PtSe 2 , the intensity of its SHG signal also displays polarization-dependent characteristics.As depicted in Figure 4(d), the polarizationdependent SHG intensity in layered PtSe 2 I SHG in 1T-type PtSe 2 can be fitted as [56] I SHG ∝ I max | cos(3)| 2 , where I max refers to the maximum SHG intensity.The polarization-dependent SHG exhibits a six-petal shape, corresponding to the in-plane threefold rotational symmetry of PtSe 2 .Since SHG intensity is highly sensitive to the crystal symmetry and orientation, by measuring the SHG signal with different incident polarization angles, one can extract valuable information about the crystal orientation of PtSe 2 at a macro scale.

Conclusions
In summary, the layer-dependent second-order nonlinear optical response in 2D PtSe 2 has been explored with intriguing results.Intense SHG is prominently observed in few layers of PtSe 2 .Notably, the strongest SHG intensity is found in 4-layer PtSe 2 , surpassing the SHG response of exfoliated MoS 2 monolayers when excited by a pulsed laser at 1064 nm by nearly two orders of magnitude.Combined with its excellent air-stability, these findings underscore the significant potential of PtSe 2 , especially in its 4-layer form, for ultrathin nonlinear optical applications.The unique layer-dependent SHG behavior of PtSe 2 opens new avenues for exploring and harnessing its nonlinear optical properties for advanced photonic technologies.
Research funding: This work was funded by the Taishan Scholar Program of Shandong Province (tspd20210303).Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.Conflict of interest: Authors state no conflicts of interest.Informed consent: Informed consent was obtained from all individuals included in this study.

Figure 1 (
Figure 1(a) and (b) present the crystal structure of van der Waals PtSe 2 , illustrating its distinctive atomic arrangement characterized by layers of atoms arranged in a typical 1T-type hexagonal crystal structure with the P3m1 space group.Each layer consists of one platinum atom sandwiched between two selenium atoms, tightly bonded through covalent interactions within the layer, while weak Van Der Waals forces maintain cohesion between adjacent layers.In contrast to conventional transition metal dichalcogenides (TMDs), PtSe 2 demonstrates significantly stronger interlayer interactions, as evidenced by its calculated interlayer energy of 0.342 eV per unit cell[51].Consequently, the mechanical exfoliation of layered PtSe 2 flakes using conventional methods proves challenging.To address this, the developed gold-assisted mechanical exfoliation method[51]-[53] is employed to exfoliate a PtSe 2 single-crystal (purchased from 2D Semiconductors) into layered PtSe 2 flakes.
) displays an optical microscope image of the exfoliated 2D PtSe 2 on a silicon substrate.Lighter colors indicate thinner layers, with the white dashed box region highlighting

Figure 1 :
Figure 1: Crystallographic structure and AFM characerization of layered-PtSe 2 .(a) and (b) Indicate the lattice structure of the layered PtSe 2 .Blue and yellow globes denote the Pt and Se atoms, respectively.(c) The optical microscope image of gold-assisted mechanically exfoliated few-layer PtSe 2 .(d) The AFM image of layered PtSe 2 in box region denoted in (c).The inset demonstrates a measured height of ∼1 nm, which corresponds to the thickness of bilayer PtSe 2 .
(a).The test conditions are configured with an input power of 1 mW and an integration time of 5 s.The inset shows an optical microscope image of the tested sample with arrows indicating the test locations.This intense SHG demonstrates PtSe 2 as a promising candidate for ultrathin nonlinear optical materials in various applications.By examining the SHG intensity maps with varying pump light intensities, we observe a slope close to 2 on logarithmic coordinates (Figure 4(b)),

Figure 3 :
Figure 3: The optical microscope image of exfoliated layered PtSe 2 and corresponding SHG mapping figures.(a) The optical microscope image of the layered PtSe 2 including monolayer, bilayer, and 4-layer PtSe 2 , as indicated by the white arrow.(b) The SHG mapping of the box region.The 4-layer PtSe 2 exhibits a strong SHG intensity, while the monolayer PtSe 2 exhibits a weak SHG response.(c) The optical microscope image of layered PtSe 2 consisting of bilayer, 3-layer, 4-layer, and 6-layer PtSe 2 .(d) The SHG mapping of the box region in (c).The 4-layer PtSe 2 exhibits a relatively strong intensity.

Figure 4 :
Figure 4: SHG property of two-dimensional PtSe 2 .(a) The SHG intensity comparison of 4-layer PtSe 2 and MoS 2 monolayer.Insets are optical microscope images of mechanically exfoliated 4-layer PtSe 2 and monolayer MoS 2 .(b) The SHG intensity as a function of the pump power in logarithmic coordinates.(c) The SHG intensity with different layer numbers.(d) The polarization-dependent SHG intensity and its fitting curve.