In-Plane Sliding Ferroelectricity Realized in Penta-PdSe2/Penta-PtSe2 van der Waals Heterostructure

Different from conventional 2D sliding ferroelectrics with polarization switchable in the out-of-plane via interlayer sliding, we show the existence of in-plane sliding ferroelectricity in a bilayer of a pentagon-based van der Waals heterostructure formed by vertically stacking an experimentally synthesized penta-PdSe2 sheet and a crystal lattice well-matched penta-PtSe2 sheet. From the 128 sliding patterns, four stable configurations are found that exhibit in-plane sliding ferroelectricity with an ultralow polarization switching barrier of 1.91 meV/atom and a high ferroelectric polarization of ±17.11 × 10-10 C m-1. Following the ferroelectric transition among the stable sliding configurations, significant changes in carrier mobility, electrical conductivity, and second harmonic generation are identified. In particular, the ferroelectric stacking configurations are found to possess a negative Poisson's ratio, facilitating the experimental characterization of the sliding ferroelectric effect. This study demonstrates that pentagonal sheets can be used to realize 2D in-plane sliding ferroelectrics going beyond the existing ones.

Out-of-plane Emission Dipole of Second Harmonic Generation in Odd- and Even-layered vdWs Janus Nb3SeI7

Integration of atomically thin nonlinear optical (NLO) devices demands an out-of-plane (OP) emission dipole of second harmonic generation (SHG) to enhance the spontaneous emission for nanophotonics. However, the research on van der Waals (vdWs) materials with an OP emission dipole of SHG is still in its infancy. Here, by coupling back focal plane (BFP) imaging with numerical simulations and density functional theory (DFT) calculations, we demonstrate that vdWs Janus Nb3SeI7, ranging from bulk to the monolayer limit, exhibits a dominant OP emission dipole of SHG owing to the breaking of the OP symmetry. Explicitly, even-layered Nb3SeI7 with C6v symmetry is predicted to exhibit a pure OP emission dipole attributed to the only second-order susceptibility coefficient χzxx. Meanwhile, although odd-layered Nb3SeI7 with C3v symmetry has both OP and IP dipole components (χzxx and χyyy), the value of χzxx is 1 order of magnitude greater than that of χyyy, leading to an approximate OP emission dipole of SHG. Moreover, the crystal symmetry and OP emission dipole can be preserved under hydrostatic pressure, accompanied by the enhanced χzxx and the resulting 3-fold increase in SHG intensity. The reported stable OP dipole in 2D vdWs Nb3SeI7 can facilitate the rapid development of chip-integrated NLO devices.

Breaking Through the Trade-Off Between Wide Band Gap and Large SHG Coefficient in Mercury-Based Chalcogenides for IR Nonlinear Optical Application

It is substantially challenging for non-centrosymmetric (NCS) Hg-based chalcogenides for infrared nonlinear optical (IR-NLO) applications to realize wide band gap (Eg > 3.0 eV) and sufficient phase-matching (PM) second-harmonic-generation intensity (deff > 1.0 × benchmark AgGaS2 ) simultaneously due to the inherent incompatibility. To address this issue, this work presents a diagonal synergetic substitution strategy for creating two new NCS quaternary Hg-based chalcogenides, AEHgGeS4 (AE = Sr and Ba), based on the centrosymmetric (CS) AEIn2 S4 . The derived AEHgGeS4 displays excellent NLO properties such as a wide Eg (≈3.04-3.07 eV), large PM deff (≈2.2-3.0 × AgGaS2 ), ultra-high laser-induced damage threshold (≈14.8-15 × AgGaS2 ), and suitable Δn (≈0.19-0.24@2050 nm), making them highly promising candidates for IR-NLO applications. Importantly, such excellent second-order NLO properties are primarily attributed to the synergistic combination of tetrahedral [HgS4 ] and [GeS4 ] functional primitives, as supported by detailed theoretical calculations. This study reports the first two NCS Hg-based materials with well-balanced comprehensive properties (i.e., Eg > 3.0 eV and deff > 1.0 × benchmark AgGaS2 ) and puts forward a new design avenue for the construction of more efficient IR-NLO candidates.

Investigation of nonlinear optical properties in α-A2BB'O6 (A = Li, Na, K; B = Ti, Zr, Hf; B' = Se, Te) by first-principles calculations

Nonlinear optical (NLO) crystals based on oxides typically have wide bandgaps and large laser damage thresholds (LDTs), which are important for generating high-power and continuous terahertz radiation. Recently, a new family of NLO materials α-A2BB'O6 including Li2TiTeO6 (LTTO) with a strong second harmonic generation (SHG) efficiency of 26 × KH2PO4 (KDP) and a large LDT of 550 MW cm-2 were reported. Herein, we systematically study the electronic structures and NLO properties of α-A2BB'O6 (A = Li, Na, K; B = Ti, Zr, Hf; B' = Se, Te) to explore the relationship between the structure and SHG coefficient. First, 15 members of the A2BB'O6 family are demonstrated to be highly stable and NLO materials, excluding K2TiTeO6, K2TiSeO6 and K2ZrSeO6. Then, the electronic band structure, dipole moment and distortion of BO6/B'O6 octahedrons, SHG coefficient and terahertz absorption spectrum are calculated comprehensively with the element variation of A-site, B-site and B'-site. Finally, the magnitude of the SHG coefficient is found to be directly proportional to the value of total dipole moment and distortion, and inversely proportional to the bandgap value. Most importantly, among the A2BB'O6 materials, K2HfSeO6 shows the smallest direct bandgap of 2.99 eV, the largest SHG coefficient d33 of about 5 × LTTO and low terahertz absorbance from 0.1 to 9 THz. Our results provide new NLO crystals that may have potential application in terahertz radiation sources and other nonlinear electronics.

Three-dimensional porous borocarbonitride composed of pentagonal motifs as a high-performance pyroelectric material

Pyroelectric materials have been attracting significant attention due to their intrinsic and permanent polarization, where the induced polarization is not associated with specific conditions, such as ferroelectric phase transition, strain gradient, dopants, and electric field. Thus, these materials have great potential for wide applications in energy conversion. Here, we propose a new 3D porous borocarbonitride termed PH-BCN, which is composed of pentagonal motifs with intrinsic polarization along the [0001] direction. Based on first-principles calculations, we show that PH-BCN possesses a record high longitudinal electromechanical coupling coefficient with the value of k33 = 97.99%, a remarkably strong SHG response (χ(2)xzx(0) = χ(2)yzy(0) = χ(2)zxx(0) = χ(2)zyy(0) = -6.23 pm V-1 and χ(2)zzz(0) = 21.21 pm V-1), and a record high shift current value of 908.58 μA V-2 due to the intrinsic vertical polarization. This study expands the family of pentagon-based materials, and may open a new frontier in the design of high-performance pyroelectric materials as well.

Rational Design of a Rare-Earth Oxychalcogenide Nd3 [Ga3 O3 S3 ][Ge2 O7 ] with Superior Infrared Nonlinear Optical Performance

Inorganic chalcogenides have been studied as the most promising infrared (IR) nonlinear optical (NLO) candidates for the past decades. However, it is proven difficult to discover high-performance materials that combine the often-incompatible properties of large energy gap (E_g ) and strong second harmonic generation (SHG) response (d_eff ), especially for rare-earth chalcogenides. Herein, centrosymmetric Cs₃ [Sb₃ O₆ ][Ge₂ O₇ ] is selected as a maternal structure and a new noncentrosymmetric rare-earth oxychalcogenide, namely, Nd₃ [Ga₃ O₃ S₃ ][Ge₂ O₇ ], is successfully designed and obtained by the module substitution strategy for the first time. Especially, Nd₃ [Ga₃ O₃ S₃ ][Ge₂ O₇ ] is the first case of breaking the trade-off relationship between wide E_g (>3.5 eV) and large d_eff (>0.5 × AgGaS₂ ) in rare-earth chalcogenide system, and thus displays an outstanding IR-NLO comprehensive performance. Detailed structure analyses and theoretical studies reveal that the NLO effect originates mainly from the cooperation of heteroanionic [GaO₂ S₂ ] and [NdO₂ S₆ ] asymmetric building blocks. This work not only presents an excellent rare-earth IR-NLO candidate, but also plays a crucial role in the rational structure design of other NLO materials in which both large E_g and strong d_eff are pursued.

First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals

Using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ⁽²⁾, values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ⁽²⁾ calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree-Fock (HF) exchange on the amplitude but also on the sign on the χ⁽²⁾ tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the sign reversal effects and the non-monotonic behavior of the χ⁽²⁾ tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χ_ZXX ⁽²⁾ of LiNbO₃. The agreement is more questionable for χ_ZZZ ⁽²⁾ of LiNbO₃ whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.

New lead-iodide formates with a strong second-harmonic generation response and suitable birefringence obtained by the substitution strategy

Nonlinear optical (NLO) crystals featuring a strong second-harmonic generation (SHG) response and suitable birefringence to achieve phase-matching are in urgent demand in industrial and commercial applications. Based on the substitution strategy, two new NLO lead-iodide formates, K₂[PbI₂(HCOO)₂] and Rb₂[PbI₂(HCOO)₂], have been successfully synthesized using a moderate mixed-solvothermal method. K₂[PbI₂(HCOO)₂] and Rb₂[PbI₂(HCOO)₂] exhibit strong phase-matching SHG responses of 8 and 6.8 × KDP, respectively, a suitable birefringence and transparent window covering most of the visible light and mid-IR region. Crystal structures and theoretical calculations unveil that the origins of the strong SHG response and suitable birefringence can be credibly attributed to the oriented arrangement of the highly distorted [PbI₂O₄] hexa-coordinated polyhedra, which are consistent in their local dipole moments, as well. This research provides a new strategy to explore high-performance NLO crystals.

Hydrogen Bond-Driven Order-Disorder Phase Transition in the Near-Room-Temperature Nonlinear Optical Switch [Ag(NH3)2]2SO4

Herein, we report a near-room-temperature nonlinear optical (NLO) switch material, [Ag(NH₃)₂]₂SO₄, exhibiting switching performance with strong room-temperature second harmonic generation (SHG) intensity that outperforms the UV-vis spectral region industry standard KH₂PO₄ (1.4 times stronger). [Ag(NH₃)₂]₂SO₄ undergoes a reversible phase transition (T _c = 356 K) from the noncentrosymmetric room-temperature phase (P4̅2₁ c, RTP) to a centrosymmetric high-temperature phase (I4/mmm, HTP) where both the SO₄ ^2- anions and [Ag(NH₃)₂]⁺ cations are highly disordered. The weakening of hydrogen bond interactions in the HTP is also evidenced by the lower energy shift of the stretching vibration of the N-H···O bonds revealed by the in situ FT-IR spectra. Such weakening leads to an unusual negative thermal expansion along the c axis (-3%). In addition, both the atomic displacement parameters of the single-crystal diffraction data and the molecular dynamics-simulated mean squared displacements suggest the motions of the O and N atoms. Such a structural disorder not only hinders the phonon propagation and dramatically drops the thermal conductivity to 0.22 W m^-1 K^-1 at 361 K but also significantly weakens the optical anisotropy and SHG as verified by the DFT theoretical studies.

Quaternary Noncentrosymmetric Rare-Earth Sulfides Ba4RE2Cd3S10 (RE = Sm, Gd, or Tb): A Joint Experimental and Theoretical Investigation

Multinary rare-earth chalcogenides with d-block transition metals have attracted considerable attention owing to their intriguing structural architectures and promising practical applications. In this work, three quaternary rare-earth sulfides, Ba₄RE₂Cd₃S₁₀ (RE = Sm, Gd, or Tb), have been obtained by the high-temperature solid-state method. These compounds are isostructural and belong to the noncentrosymmetric orthorhombic space group Cmc2₁ (No. 36). The basic structural unit contains unique two-dimensional anionic [RE₂Cd₃S₁₀]^8- layers, which are separated by Ba²⁺ cations. Remarkably, Ba₄Sm₂Cd₃S₁₀ exhibits a high second-harmonic-generation intensity (1.8 times that of AgGaS₂) and a significantly higher laser-induced damage threshold (14.3 times that of AgGaS₂), which is the first case possessing an infrared (IR) nonlinear optical (NLO) property in the quaternary AE/RE/TM/Q (AE = alkaline-earth metals; RE = rare-earth metals; TM = d-block transition metals; and Q = chalcogen) systems. Moreover, theoretical investigations of the structure-property relationship indicate that the combined action of various types of NLO-active units makes the main contribution to the SHG activity. This discovery may shed light on broadening the frontiers of IR-NLO materials.

Anisotropic Second-Harmonic Generation Induced by Reduction of In-Plane Symmetry in 2D Materials with Strain Engineering

Strain engineering is an attractive method to induce and control anisotropy for polarized optoelectronic applications with two-dimensional (2D) materials. Herein, we have investigated the nonlinear optical coefficient dispersion relationship and the second-harmonic generation (SHG) pattern evolution under the uniaxial strains for graphene, WS₂, GaSe, and In₂Se₃ monolayers. The uniaxial strain can break the in-plane symmetry of 2D materials, leading to both trade-off breaking of the nonlinear coefficient and new emergent nonlinear coefficients. In such a case, a classical sixfold ϕ-dependent SHG pattern is transformed into a distorted sixfold SHG pattern under the strain. Due to the lattice symmetry breaking and the uneven charge density distribution in strained 2D materials, the SHG patterns also depend on the excitation photon energy. The results could give a guide for the SHG pattern analysis in experiments, suggesting strain engineering on 2D materials for the tunable anisotropy in polarized and flexible nonlinear optical devices.

Dispersion Property and Evolution of Second Harmonic Generation Pattern in Type-I and Type-II van der Waals Heterostructures

Dispersion property and second harmonic generation (SHG) pattern of novel two-dimensional (2D) van der Waals heterostructures (vdWHs) is of great significance not only for the characterization of material symmetry but also for understanding nonlinear photophysical phenomena. Herein, we demonstrate the SHG response of 2D type-I (MoTe₂/WSe₂) and type-II (MoSe₂/WSe₂) band alignment of vdWHs. In the dispersion relation of the second-order nonlinear coefficient, the pronounced peaks of the d₁₆ element for both vdWHs are mainly contributed by resonance in the interband transition processes, whereas other elements are derived from the intraband transition processes because of the highly efficient charge transfer from WSe₂ to MoTe₂ in type-I vdWHs and the ultrafast charge separation between WSe₂ and MoSe₂ in type-II vdWHs, respectively. Besides, more nonzero nonlinear coefficient elements can participate in a nonlinear response at the oblique incidence, to which special attention needs paid. The polarization angle α-dependent SHG patterns display a rotational fourfold symmetry, whereas the azimuthal angle ϕ-dependent SHG patterns show sixfold symmetry for both type-I and type-II vdWHs at any wavelength under normal incidence. Under oblique incidence, the α-dependent (ϕ-dependent) SHG patterns will reduce to twofold (threefold) symmetry for both vdWHs. The results highlight the potential to deterministically engineer novel nonlinear optical properties for tunable anisotropic applications of nonlinear optoelectronic devices based on vdWHs.

Struvite-type AMgPO4·6H2O (A = NH4, K): Two Natural Deep-Ultraviolet Transparent Nonlinear Optical Crystals

Deep-ultraviolet (DUV) nonlinear optical (NLO) materials play vital roles in diverse fields. Unfortunately, only the KBe₂BO₃F₂ crystal has found commercial applications so far. Therefore, the discovery of new DUV NLO crystals is still urgent. As we all know, digging into the properties of existing crystals is also an effective way to obtain new NLO crystals. Herein, two natural asymmetric orthophosphates AMgPO₄·6H₂O (A = NH₄, K) are proposed. Although their structures and some properties such as infrared spectra, thermal properties, and dielectric properties have been previously characterized, their NLO properties have not been reported. Thus, in this work, these two natural DUV transparent orthophosphates NH₄MgPO₄·6H₂O (NMP) and KMgPO₄·6H₂O (KMP) were successfully acquired by a simple slow evaporation method. The single-crystal X-ray diffraction data indicate that NMP and KMP are isomorphic and that both belong to the Pmn2₁ space group of the orthorhombic system. Remarkably, NMP and KMP possess short cutoff edges below 190 nm, and their second-harmonic generation (SHG) efficiencies are 0.62 and 0.80 times that of KH₂PO₄(KDP), respectively; furthermore, they can achieve type-I phase matching at 1064 nm.

Accurate electronic properties and non-linear optical response of two-dimensional MA2Z4

Two-dimensional MA2Z4 (M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, or Cr; A = Si or Ge; Z = N, P, or As) is a new lead in the 2D family, because it exhibits versatile properties by tuning the components M, A and Z. However, theoretical studies on MA2Z4 are quite limited, and electronic properties are mainly studied by standard DFT levels, which seriously underestimates the band gap. Here, we systematically investigated the electronic properties and nonlinear optical response of MA2Z4 using a hybrid HSE06 functional. It was found that replacing component Z changes the lattice constant most, while the lattice influence by component M substitution is only slight. We showed that the gap difference between PBE and HSE06 is generally about 30% but can be up to 101%. (MIV = Hf, Ti, or Zr)Si2N4 possesses multi-valley characteristics. Furthermore, the second-harmonic generation (SHG) responses of various MA2Z4 composites were also calculated. Three non-zero elements of second order non-linear susceptibilities are revealed for MA2Z4 with the relationship: d16 = d21 = d22, indicating that MA2Z4 belongs to the D3H1 space group. HfSi2N4 possesses a multi-valley characteristic, and exhibits the largest susceptibility under broad wavelengths and the value of d21 reaches 3697.04 pm V-1 at band gap resonance energy. Intriguingly, the non-linear coefficients of MoSi2P4 and MoSi2As4 in the IR region are two orders of magnitude larger than those of other well-known non-linear crystals, such as LiGaS2 and BaAl4S7. We further explored the anisotropic SHG response by the polar plot of intensity under different incident light into MA2Z4. Our work provides theoretical guidelines for further experimental explorations of MA2Z4 and paves the way for its utilization in non-linear optic devices.

Nonlinear Optical Response in Graphene/WX2 (X = S, Se, and Te) van der Waals Heterostructures

Light-frequency conversion based on two-dimensional (2D) materials is of great importance for modern nano- and integrated photonics. Herein, we report both the intrinsic (from the pure WX₂ (X = S, Se, and Te)) and extrinsic (from the interface of graphene/WX₂) second-order nonlinear coefficient tensor from graphene/WX₂ van der Waals (vdW) heterostructures by first-principles calculations. The prominent peaks in the dispersion relation of the intrinsic second-order nonlinear coefficient in monolayer WX₂ are due to the Van Hove singularity in the high-symmetry point or along the high-symmetry line with high joint density of states. The enhanced nonlinear optical response in the infrared band can be achieved in graphene/WS₂ vdW heterostructures, resulting from the interlayer charge transfer between graphene and WS₂. The value of the intrinsic second-order nonlinear coefficients of graphene/WSe₂ vdW heterostructures is 1.5 times larger than that of pure monolayer WSe₂ at the band gap energy of monolayer WSe₂ because of the enhanced carrier generation after the heterostructure formation. Different from pure monolayer WX₂, azimuthal angle-dependent second harmonic generation from graphene/WX₂ vdW heterostructures exhibits extraordinary rotational symmetry at different photon energies, which can be used to deduce the extrinsic second-order nonlinear coefficient. These results pave the way for the nonlinear optical coefficient design based on 2D heterostructures for nonlinear nanophotonics and integrated devices.

Planar graphitic ZnS, buckling ZnS monolayers and rolled-up nanotubes as nonlinear optical materials: first-principles simulation

Nonlinear optical (NLO) materials have an ability to generate new coherent light. At the present stage, three dimensional (3D) mid-infrared NLO materials suffer from various deficiencies such as low laser damage thresholds (LDTs) for AgGaQ₂ (Q = S, Se); the band gaps of most intensively studied two-dimensional (2D) NLO materials are not wide enough to avoid two-photon absorption (TPA); a steady NLO property regardless of diameter and chirality is absent in one-dimensional (1D) single-walled nanotubes (SWNTs). In this research, the electronic and second harmonic generation (SHG) properties of planar graphitic ZnS (g-ZnS) monolayer, buckling reconstructed ZnS (R-ZnS) monolayer which is synthesized in a recent experiment, and rolled-up SWNTs are investigated with first-principles simulations. Theoretical results suggest the SHG coefficients of planar g-ZnS, buckling R-ZnS and rolled-up SWNTs are comparable with that of AgGaS₂ crystals. The band gaps of planar g-ZnS and ZnS SWNTs are ∼3.8 eV, and that of buckling R-ZnS is as wide as ∼4.0 eV, indicating high LDTs and reduced TPA as NLO materials. The TPA edges can be further blue shifted by using incident light beams with a polarized electric field perpendicular to buckling R-ZnS. On the other hand, the TPA edges of ZnS SWNTs are nearly not affected by diameter and chirality. The SHG coefficients of ZnS SWNTs are much less influenced by chirality and diameter than those of SiC, GeC and BN SWNTs. Therefore, they are superior ultrathin NLO materials, and especially have a potential application in the mid-infrared regime where high-quality NLO crystals are emergently needed.

Contradictory large SHG coefficients and wide bandgaps are simultaneously discovered in planar graphitic ZnS, buckling ZnS monolayers and rolled-up nanotubes.

Indium selenide monolayer: a two-dimensional material with strong second harmonic generation

The In₂Se₃ monolayer may be a material with the strongest SHG response among IIIA–VIA semiconductors reported to date.

Theoretical perspectives on the structure, electronic, and optical properties of titanosilicates Li2M4[(TiO)Si4O12] (M = K+, Rb+)

The structure–property relationship of new transition-metal silicates, used as promising SHG materials, was unraveled using theoretical perspectives.

Second-order nonlinear optical properties of bulk GeC polytypes, g-GeC and corresponding nanotubes: first-principles calculations

GeC nanotubes possess a strong second-order NLO response. Its origin is the high density of states near the VBM.

Peculiar electronic, strong in-plane and out-of-plane second harmonic generation and piezoelectric properties of atom-thick α-M2X3 (M = Ga, In; X = S, Se): role of spontaneous electric dipole orientations

Single- and few-layer α-M₂X₃ nanosheets exhibit out-of-plane SHG and piezoelectric properties, which can be tuned by switching spontaneous polarizations.

Layer-independent and layer-dependent nonlinear optical properties of two-dimensional GaX (X = S, Se, Te) nanosheets

The magnitude of SHG coefficients for monolayers and AAA gets very close, while it becomes about 1/3 for ABA.