Universal Imaging of Full Strain Tensor in 2D Crystals with Third-Harmonic Generation

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

A pair of ionic 1D Cu(II) chain enantiomers simultaneously displaying large second- and third-harmonic generation responses

By employing enantiomerically pure mono-bidentate N-donors (LR/LS) as chiral bridging ligands to react with Cu(ClO4)2(H2O)6 in CH3CN-DMF mixed solvent, respectively, a pair of ionic one-dimensional (1D) Cu(II) chain enantiomers formulated as {[CuLR(CH3CN)(DMF)H2O](ClO4)2}n/{[CuLS(CH3CN)(DMF)H2O](ClO4)2}n (D-1/L-1) were isolated and structurally characterized, where LR/LS = (-)/(+)-4,5-pinenepyridyl-2-pyrazine. They crystallize in the noncentrosymmetric (NCS) P212121 space group of an orthorhombic system due to the introduction of chiral LR/LS, and the ClO4- groups as counteranions reside in crystal lattices, thus leading to charge separation with large dipole moments in their molecular structures. Based on crystal samples, investigation on their nonlinear optical (NLO) behaviors showed that D-1 and L-1 display simultaneously much larger second- and third-harmonic generation (SHG and THG) responses than their analogues based on the same chiral N-donors (LR/LS) and Cu(NO3)2(H2O)3 with NO3- acting as the coordination group to bind Cu(II) ions. The SHG intensities of D-1/L-1 are 0.62/0.60 × KDP (KH2PO4), and THG intensities of D-1/L-1 are 238/228 × α-SiO2. Our finding indicates that coordination polymers (CPs) with charge separation and NCS structures, i.e., ionic CPs with NCS arrangements are the ideal NLO crystalline materials for the simultaneous observation of large SHG and THG responses, thus providing a new approach to obtain NLO-active CP crystalline materials with high-performance SHG and THG responses.

Nonlinear Optical Properties from Engineered 2D Materials

Two-dimensional (2D) materials with atomic thickness, tunable light-matter interaction, and significant nonlinear susceptibility are emerging as potential candidates for new-generation optoelectronic devices. In this review, we briefly cover the recent research development of typical nonlinear optic (NLO) processes including second harmonic generation (SHG), third harmonic generation (THG), as well as two-photon photoluminescence (2PPL) of 2D materials. Nonlinear light-matter interaction in atomically thin 2D materials is important for both fundamental research and future optoelectronic devices. The NLO performance of 2D materials can be greatly modulated with methods such as carrier injection tuning, strain tuning, artificially stacking, as well as plasmonic resonant enhancement. This review will discuss various nonlinear optical processes and corresponding tuning methods and propose its potential NLO application of 2D materials.

Coherent modulation of chiral nonlinear optics with crystal symmetry

Light modulation is of paramount importance for photonics and optoelectronics. Here we report all-optical coherent modulation of third-harmonic generation (THG) with chiral light via the symmetry enabled polarization selectivity. The concept is experimentally validated in monolayer materials (MoS₂) with modulation depth approaching ~100%, ultra-fast modulation speed (<~130 fs), and wavelength-independence features. Moreover, the power and polarization of the incident optical beams can be used to tune the output chirality and modulation performance. Major performance of our demonstration reaches the fundamental limits of optical modulation: near-unity modulation depth, instantaneous speed (ultra-fast coherent interaction), compact footprint (atomic thickness), and unlimited operation bandwidth, which hold an ideal optical modulation solution for emerging and future nonlinear optical applications (e.g., interconnection, imaging, computing, and quantum technologies).

Polarimetric photoluminescence microscope for strain imaging on semiconductor devices

Anisotropic strain induces a partial linear polarization of the photo-luminescence (PL) emitted by cubic semiconductor crystals such as GaAs or InP. This paper thus presents a polarimetric PL microscope dedicated to the characterization of semiconductor devices. The anisotropic strain is quantified through the determination of the degree of linear polarization (DOLP) of the PL and the angle of this partial linear polarization. We illustrate the possibilities of this tool by mapping the anisotropic strain generated in GaAs by the presence of a stressor film at its surface, that is, a microstructure defined in a dielectric thin film (SiNx) that has been deposited with a built-in stress and shaped into a narrow stripe by lithography and etching. Our setup shows a DOLP resolution as low as 4.5×10^-4 on GaAs.

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.

Multifunctional DyIII Enantiomeric Pairs Showing Enhanced Photoluminescences and Third-Harmonic Generation Responses through the Coordination Role of Homochiral Tridentate N,N,N-Pincer Ligands

By utilizing Dy(hfac)₃(H₂O)₂ to react with enantiomerically pure tridentate N,N,N-pincer ligands, namely (-)/(+)-2,6-bis(4',5'-pinene-2'-pyridyl)pyridine (L_R and L_S), respectively, homochiral Dy^III enantiomeric pairs formulated as Dy(hfac)₃L_R/Dy(hfac)₃L_S (R-1/S-1) (hfac^- = hexafluoroacetylacetonate) were achieved and structurally characterized. Meanwhile, their magnetic, photoluminescent (PL), and chiroptical properties were probed. The PL test results indicate that the precursor Dy(hfac)₃(H₂O)₂ only shows very weak emission, while R-1 exhibits characteristic Dy^III f-f transition emission bands at room temperature. Furthermore, the nonlinear optical responses of Dy(hfac)₃(H₂O)₂, L_R/L_S, and R-1/S-1 were investigated in detail based on crystalline samples. The results reveal that L_R and L_S present the coexistence of second- and third-harmonic generation (SHG and THG) responses with more intense signals for SHG responses; and Dy(hfac)₃(H₂O)₂ merely displays weak THG responses, while R-1 and S-1 also only exhibit THG responses. However, the THG intensities of R-1 and S-1 are more than six times larger than that of Dy(hfac)₃(H₂O)₂ under the identical measurement conditions. These results demonstrate that introducing homochiral N,N,N-pincer ligands to replace two H₂O molecules of Dy(hfac)₃(H₂O)₂ results in significant improvements of both PL performances and THG responses of resultant R-1/S-1 enantiomers. R-1 and S-1 integrate PL, THG, and chiral optical activity in one molecule, suggesting their multifunctional merits. In particular, a convenient method is introduced to simultaneously test THG and SHG responses of molecular materials based on crystalline samples in this work.

Strained Epitaxy of Monolayer Transition Metal Dichalcogenides for Wrinkle Arrays

Wrinkling two-dimensional (2D) transition metal dichalcogenides (TMDCs) provides a mechanism to adjust the physical and chemical properties as per need. Traditionally, TMDCs wrinkles achieved by transferring exfoliated materials on prestretched polymer suffer from poor control and limited sample area, which significantly hinders desirable applications. Herein, we fabricate large-area monolayer TMDCs wrinkle arrays directly on the m-quartz substrate using strained epitaxy. The uniaxial thermal expansion coefficient mismatch between the substrate and TMDCs materials enables the generation of large uniaxial thermal strain. By quenching the TMDCs after growth, this uniaxial thermal strain can be quickly released as a form of wrinkle arrays along the [0001]_quartz direction. Using WS₂ as a model system, the size of as-grown wrinkles can be finely modulated within sub-100 nm by changing the quenching temperature. These WS₂ wrinkles can be locally folded and form various multilayer structures with odd layer numbers during the transfer process. Besides, the corrugated structures in WS₂ wrinkles induce significant changes to optical properties including anisotropic Raman response, enhanced photoluminescence, and second harmonic generation emissions. Furthermore, these wrinkle arrays exhibit enhanced chemical reactivity that can be selectively engineered to ribbon arrays with improved electrocatalytic performance. The developed strategy of strained epitaxy here should enable flexibility in the design of more sophisticated 2D-based structures, offering a simple but effective way toward the modulation of properties with enhanced performances.

Nonlinear Optical Characterization of 2D Materials

Characterizing the physical and chemical properties of two-dimensional (2D) materials is of great significance for performance analysis and functional device applications. As a powerful characterization method, nonlinear optics (NLO) spectroscopy has been widely used in the characterization of 2D materials. Here, we summarize the research progress of NLO in 2D materials characterization. First, we introduce the principles of NLO and common detection methods. Second, we introduce the recent research progress on the NLO characterization of several important properties of 2D materials, including the number of layers, crystal orientation, crystal phase, defects, chemical specificity, strain, chemical dynamics, and ultrafast dynamics of excitons and phonons, aiming to provide a comprehensive review on laser-based characterization for exploring 2D material properties. Finally, the future development trends, challenges of advanced equipment construction, and issues of signal modulation are discussed. In particular, we also discuss the machine learning and stimulated Raman scattering (SRS) technologies which are expected to provide promising opportunities for 2D material characterization.

Strain-dependent anisotropic nonlinear optical response in two-dimensional functionalized MXene Sc2CT2 (T = O and OH)

Tunable optical properties play an important role in the high performance of optoelectronic applications based on two-dimensional (2D) transition metal carbide and nitride (MXene) materials. Herein, the optical properties of functionalized MXene monolayers Sc₂CT₂ (T = O and OH) are investigated by strain engineering. The strain-dependent linear optical properties of Sc₂CT₂ possess broadband optical response due to the geometry and orbital overlap effect. The peaks from the second-order nonlinear coefficient elements d (d₁₅, d₁₆, and d₃₁) at around half the band-gap exhibit a redshift for Sc₂CO₂ (blueshift for Sc₂C(OH)₂) with the increase of strain. The strain-dependent d reveals that Sc₂CO₂ with -1268 pm V^-1 %^-1 has a larger photoelastic coefficient than that of Sc₂C(OH)₂ with -574 pm V^-1 %^-1 at 1% strain. Meanwhile, the photoelastic tensors can not only be increased but also reduced with the increase of strain due to the dispersion relation. Moreover, the azimuthal angle-dependent second harmonic generation (SHG) from strained Sc₂CT₂ monolayers depends highly on the strained states and the pumping photon energy. The results pave the way for the tunable, broadband, and anisotropic applications of nonlinear optoelectronic devices based on MXenes based on strain engineering.

2D Inorganic Bimolecular Crystals with Strong In-Plane Anisotropy for Second-Order Nonlinear Optics

2D inorganic bimolecular crystals, consisting of two different inorganic molecules, are expected to possess novel physical and chemical properties due to the synergistic effect of the individual components. However, 2D inorganic bimolecular crystals remain unexploited because of the difficulties in preparation arising from non-typical layered structures and intricate intermolecular interactions. Here, the synthesis of 2D inorganic bimolecular crystal SbI₃ ·3S₈ nanobelts via a facile vertical microspacing sublimation strategy is reported. The as-synthesized SbI₃ ·3S₈ nanobelts exhibit strong in-plane anisotropy of phonon vibrations and intramolecular vibrations as well as show anisotropic light absorption with a high dichroism ratio of 3.9. Furthermore, it is revealed that the second harmonic generation intensity of SbI₃ ·3S₈ nanobelts is highly dependent on the excitation wavelength and crystallographic orientation. This work can inspire the growth of more 2D inorganic bimolecular crystals and excite potential applications for bimolecular optoelectronic devices.

Unveiling the Fine Structural Distortion of Atomically Thin Bi2 O2 Se by Third-Harmonic Generation

Bismuth oxyselenide (Bi₂ O₂ Se), a new type of 2D material, has recently attracted increased attention due to its robust bandgap, stability under ambient conditions, and ultrahigh electron mobility. In such complex oxides, fine structural distortion tends to play a decisive role in determining the unique physical properties, such as the ferrorotational order, ferroelectricity, and magnetoelasticity. Therefore, an in-depth investigation of the fine structural symmetry of Bi₂ O₂ Se is necessary to exploit its potential applications. However, conventional techniques are either time consuming or requiring tedious sample treatment. Herein, a noninvasive and high-throughput approach is reported for characterizing the fine structural distortion in 2D centrosymmetric Bi₂ O₂ Se by polarization-dependent third-harmonic generation (THG). Unprecedentedly, the divergence between the experimental results and the theoretical prediction of the perpendicular component of polarization-dependent THG indicates a fine structural distortion, namely, a <1.4° rotation of the oxygen square in the tetragonal (Bi₂ O₂ ) layers. This rotation breaks the intrinsic mirror symmetry of 2D Bi₂ O₂ Se, eventually reducing the symmetry from the D_4h to the C_4h point group. The results demonstrate that THG is highly sensitive to even fine symmetry variations, thereby showing its potential to uncover hidden phase transitions and interacting polarized sublattices in novel 2D material systems.

Electrical Control of Interband Resonant Nonlinear Optics in Monolayer MoS2

Monolayer transition-metal dichalcogenides show strong optical nonlinearity with great potential for various emerging applications. Here we demonstrate the gate-tunable interband resonant four-wave mixing and sum-frequency generation in monolayer MoS₂. Up to 80% modulation depth in four-wave mixing is achieved when the generated signal is resonant with the A exciton at room temperature, corresponding to an effective third-order optical nonlinearity |χ⁽³⁾_eff| tuning from (∼12.0 to 5.45) × 10^-18 m²/V². The tunability of the effective second-order optical nonlinearity |χ⁽²⁾_eff| at 440 nm C-exciton resonance wavelength is also demonstrated from (∼11.6 to 7.40) × 10^-9 m/V with sum-frequency generation. Such a large tunability in optical nonlinearities arises from the strong excitonic charging effect in monolayer transition-metal dichalcogenides, which allows for the electrical control of the interband excitonic transitions and thus nonlinear optical responses for future on-chip nonlinear optoelectronics.

Engineering Phase Transformation of MoS2/RGO by N-doping as an Excellent Microwave Absorber

As a hot two-dimensional (2D) material, molybdenum disulfide has been attracting extensive attention for electromagnetic wave response applications because of its unique structure. However, the electronic conductivity of nanostructured MoS₂ needs to be optimized urgently. Here, nitrogen-doped 1T@2H-MoS₂/reduced graphene oxide (RGO) composites are effectively constructed by hydrothermal reaction and consecutive calcination under an NH₃ atmosphere. The prepared composites possess great microwave absorption (MA) performance with an expected absorption bandwidth (4.00 GHz) at the Ku band and a maximum reflection loss value (-67.77 dB), which is much better than the performance of conventional 2H-MoS₂ or 2H-MoS₂/RGO. The prominent absorption property is ascribed to the (i) unique self-assemble morphology of rose-like MoS₂ supported on 2D RGO; (ii) controllable crystalline phase switch between 2H and 1T; and (iii) brilliant energy attenuation caused by the intense multipolarization. Furthermore, the dominant MA mechanism is described as the local polarization motivated by the interaction between RGO and MoS₂. Thus, our novel structure design provides a necessary reference to achieve optimized absorption performance based on 2D materials.