Giant Optical Second Harmonic Generation in Two-Dimensional Multiferroics

Governing of the piezoelectric effect by external fields and strains

Piezoelectricity in quantum rare-earth metallic boron oxides with the coupling between magnetic, electric and elastic subsystem is studied theoretically. It is proved that the change of piezoelectric modules of the considered crystals are proportional to components of the quadrupole susceptibility, which determines the external magnetic and electric fields, strain and temperature dependences of that change. We show why holmium compounds manifest the strongest renormalization among other rare-earth ions in this family of crystals. The reason is in the structure of the low energy term of the electron configuration, depending on spins and orbital moments of 4f electrons.

Nonlinear Optical Properties of 2D Materials and their Applications

2D materials are a subject of intense research in recent years owing to their exclusive photoelectric properties. With giant nonlinear susceptibility and perfect phase matching, 2D materials have marvelous nonlinear light-matter interactions. The nonlinear optical properties of 2D materials are of great significance to the design and analysis of applied materials and functional devices. Here, the fundamental of nonlinear optics (NLO) for 2D materials is introduced, and the methods for characterizing and measuring second-order and third-order nonlinear susceptibility of 2D materials are reviewed. Furthermore, the theoretical and experimental values of second-order susceptibility χ(2) and third-order susceptibility χ(3) are tabulated. Several applications and possible future research directions of second-harmonic generation (SHG) and third-harmonic generation (THG) for 2D materials are presented.

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.

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

Can 2D Semiconductors Be Game-Changers for Nanoelectronics and Photonics?

2D semiconductors have interesting physical and chemical attributes that have led them to become one of the most intensely investigated semiconductor families in recent history. They may play a crucial role in the next technological revolution in electronics as well as optoelectronics or photonics. In this Perspective, we explore the fundamental principles and significant advancements in electronic and photonic devices comprising 2D semiconductors. We focus on strategies aimed at enhancing the performance of conventional devices and exploiting important properties of 2D semiconductors that allow fundamentally interesting device functionalities for future applications. Approaches for the realization of emerging logic transistors and memory devices as well as photovoltaics, photodetectors, electro-optical modulators, and nonlinear optics based on 2D semiconductors are discussed. We also provide a forward-looking perspective on critical remaining challenges and opportunities for basic science and technology level applications of 2D semiconductors.

Optical Second Harmonic Generation of Low-Dimensional Semiconductor Materials

In recent years, the phenomenon of optical second harmonic generation (SHG) has attracted significant attention as a pivotal nonlinear optical effect in research. Notably, in low-dimensional materials (LDMs), SHG detection has become an instrumental tool for elucidating nonlinear optical properties due to their pronounced second-order susceptibility and distinct electronic structure. This review offers an exhaustive overview of the generation process and experimental configurations for SHG in such materials. It underscores the latest advancements in harnessing SHG as a sensitive probe for investigating the nonlinear optical attributes of these materials, with a particular focus on its pivotal role in unveiling electronic structures, bandgap characteristics, and crystal symmetry. By analyzing SHG signals, researchers can glean invaluable insights into the microscopic properties of these materials. Furthermore, this paper delves into the applications of optical SHG in imaging and time-resolved experiments. Finally, future directions and challenges toward the improvement in the NLO in LDMs are discussed to provide an outlook in this rapidly developing field, offering crucial perspectives for the design and optimization of pertinent devices.

Tailoring Ultrafast Near-Band Gap Photoconductive Response in GeS by Zero-Valent Cu Intercalation

Zero-valent intercalation of atomic metals into the van der Waals gap of layered materials can be used to tune their electronic, optical, thermal, and mechanical properties. Here, we report the impact of intercalating ∼3 atm percent of zero-valent copper into germanium sulfide (GeS). Advanced many-body calculations predict that copper introduces quasi-localized intermediate band states, and time-resolved THz spectroscopy studies demonstrate that those states have prominent effects on the photoconductivity of GeS. Cu-intercalated GeS exhibits a faster rise of transient photoconductivity and a shorter lifetime of optically injected carriers following near-gap excitation with 800 nm pulses. At the same time, Cu intercalation improves free carrier mobility from 1100 to 1300 cm2 V-1 s-1, which we attribute to the damping of acoustic phonons observed in Brillouin scattering and consequent reduction of phonon scattering.

Anisotropic Strain-Tailoring Nonlinear Optical Response in van der Waals NbOI2

Two-dimensional (2D) NbOI2 demonstrates significant second-harmonic generation (SHG) with a high conversion efficiency. To unlock its full potential in practical applications, it is desirable to modulate the SHG behavior while utilizing the intrinsic lattice anisotropy. Here, we demonstrate direction-specific modulation of the SHG response in NbOI2 by applying anisotropic strain with respect to the intrinsic lattice orientations, where more than 2-fold enhancement in the SHG intensity is achieved under strain along the polar axis. The strain-driven SHG evolution is attributed to the strengthened built-in piezoelectric field (polar axis) and the enlarged Peierls distortions (nonpolar axis). Moreover, we provide quantifications of the correlation between strain and SHG intensity in terms of the susceptibility tensor. Our results demonstrate the effective coupling of orientation-specific strain to the anisotropic SHG response through the intrinsic polar order in 2D nonlinear optical crystals, opening a new paradigm toward the development of functional devices.

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.

Pressure-Induced Modulation of Tin Selenide Properties: A Review

Tin selenide (SnSe) holds great potential for abundant future applications, due to its exceptional properties and distinctive layered structure, which can be modified using a variety of techniques. One of the many tuning techniques is pressure manipulating using the diamond anvil cell (DAC), which is a very efficient in situ and reversible approach for modulating the structure and physical properties of SnSe. We briefly summarize the advantages and challenges of experimental study using DAC in this review, then introduce the recent progress and achievements of the pressure-induced structure and performance of SnSe, especially including the influence of pressure on its crystal structure and optical, electronic, and thermoelectric properties. The overall goal of the review is to better understand the mechanics underlying pressure-induced phase transitions and to offer suggestions for properly designing a structural pattern to achieve or enhanced novel properties.

Domain-dependent strain and stacking in two-dimensional van der Waals ferroelectrics

Van der Waals (vdW) ferroelectrics have attracted significant attention for their potential in next-generation nano-electronics. Two-dimensional (2D) group-IV monochalcogenides have emerged as a promising candidate due to their strong room temperature in-plane polarization down to a monolayer limit. However, their polarization is strongly coupled with the lattice strain and stacking orders, which impact their electronic properties. Here, we utilize four-dimensional scanning transmission electron microscopy (4D-STEM) to simultaneously probe the in-plane strain and out-of-plane stacking in vdW SnSe. Specifically, we observe large lattice strain up to 4% with a gradient across ~50 nm to compensate lattice mismatch at domain walls, mitigating defects initiation. Additionally, we discover the unusual ferroelectric-to-antiferroelectric domain walls stabilized by vdW force and may lead to anisotropic nonlinear optical responses. Our findings provide a comprehensive understanding of in-plane and out-of-plane structures affecting domain properties in vdW SnSe, laying the foundation for domain wall engineering in vdW ferroelectrics.

Manipulation of nonlinear optical responses in layered ferroelectric niobium oxide dihalides

Realization of highly tunable second-order nonlinear optical responses, e.g., second-harmonic generation and bulk photovoltaic effect, is critical for developing modern optical and optoelectronic devices. Recently, the van der Waals niobium oxide dihalides are discovered to exhibit unusually large second-harmonic generation. However, the physical origin and possible tunability of nonlinear optical responses in these materials remain to be unclear. In this article, we reveal that the large second-harmonic generation in NbOX2 (X = Cl, Br, and I) may be partially contributed by the large band nesting effect in different Brillouin zone. Interestingly, the NbOCl2 can exhibit dramatically different strain-dependent bulk photovoltaic effect under different polarized light, originating from the light-polarization-dependent orbital transitions. Importantly, we achieve a reversible ferroelectric-to-antiferroelectric phase transition in NbOCl2 and a reversible ferroelectric-to-paraelectric phase transition in NbOI2 under a certain region of external pressure, accompanied by the greatly tunable nonlinear optical responses but with different microscopic mechanisms. Our study establishes the interesting external-field tunability of NbOX2 for nonlinear optical device applications.

Electrostatic gating dependent multiple band alignments in ferroelectric VS2/Ga2O3 van der Waals heterostructures

Two-dimensional (2D) van der Waals (vdW) heterostructures with spontaneous intrinsic ferroelectrics play an essential role in ferroelectric memories. Also, the reversal of polarized directions induces band alignment transitions among different types to provide a new path for multifunctional devices. In this work, the structural and electronic properties of 2D VS2/Ga2O3 vdW heterostructures under different polarizations were investigated using first-principles calculations with the vdW correction of the DFT-D2 method. The results reveal that the polarized direction of a 2D Ga2O3 monolayer can cause a distinct band structure reversion from a metal to a semiconductor due to the shift of band alignment induced by the interlayer charge transfer. Moreover, the VS2/P↑ Ga2O3 heterostructures retain type-I and type-II band alignments in the majority and minority channel, respectively, under an external electric field. Interestingly, applying the external electric field for VS2/P↓ Ga2O3 heterostructures can lead to a transition from type-II to type-I in the majority channel, and from type-II to type-III in the minority channel. Our work provides a feasible way to realize 2D VS2/Ga2O3 vdW heterostructures for potential applications in ferroelectric memories and electrostatic gating dependent multiple band alignment devices.

Stacking-Controlled Growth of rBN Crystalline Films with High Nonlinear Optical Conversion Efficiency up to 1

Nonlinear optical crystals lie at the core of ultrafast laser science and quantum communication technology. The emergence of 2D materials provides a revolutionary potential for nonlinear optical crystals due to their exceptionally high nonlinear coefficients. However, uncontrolled stacking orders generally induce the destructive nonlinear response due to the optical phase deviation in different 2D layers. Therefore, conversion efficiency of 2D nonlinear crystals is typically limited to less than 0.01% (far below the practical criterion of >1%). Here, crystalline films of rhombohedral boron nitride (rBN) with parallel stacked layers are controllably synthesized. This success is realized by the utilization of vicinal FeNi (111) single crystal, where both the unidirectional arrangement of BN grains into a single-crystal monolayer and the continuous precipitation of (B,N) source for thick layers are guaranteed. The preserved in-plane inversion asymmetry in rBN films keeps the in-phase second-harmonic generation field in every layer and leads to a record-high conversion efficiency of 1% in the whole family of 2D materials within the coherence thickness of only 1.6 µm. The work provides a route for designing ultrathin nonlinear optical crystals from 2D materials, and will promote the on-demand fabrication of integrated photonic and compact quantum optical devices.

Giant Bulk Electrophotovoltaic Effect in Heteronodal-Line Systems

The realization of a giant and continuously tunable second-order photocurrent is desired for many nonlinear optical (NLO) and optoelectronic applications, which remains a great challenge. Here, based on a two-band model, we propose a concept of the bulk electrophotovoltaic effect, that is, an out-of-plane external electric field (E_{ext}) that can continuously tune in-plane shift current along with its sign flip in a heteronodal-line (HNL) system. While strong linear optical transition around the nodal loop may potentially generate giant shift current, an E_{ext} can effectively control the radius of the nodal loop, which can continuously modulate the shift-vector components inside and outside the nodal loop holding opposite signs. This concept has been demonstrated in the HNL HSnN/MoS_{2} system using first-principles calculations. The HSnN/MoS_{2} heterobilayer can not only produce a shift-current conductivity with magnitude that is one to two orders larger than other reported systems, but it can also realize a giant bulk electrophotovoltaic effect. Our finding opens new routes to create and manipulate NLO responses in 2D materials.

2D Material Infrared Photonics and Plasmonics

Two-dimensional (2D) materials including graphene, transition metal dichalcogenides, black phosphorus, MXenes, and semimetals have attracted extensive and widespread interest over the past years for their many intriguing properties and phenomena, underlying physics, and great potential for applications. The vast library of 2D materials and their heterostructures provides a diverse range of electrical, photonic, mechanical, and chemical properties with boundless opportunities for photonics and plasmonic devices. The infrared (IR) regime, with wavelengths across 0.78 μm to 1000 μm, has particular technological significance in industrial, military, commercial, and medical settings while facing challenges especially in the limit of materials. Here, we present a comprehensive review of the varied approaches taken to leverage the properties of the 2D materials for IR applications in photodetection and sensing, light emission and modulation, surface plasmon and phonon polaritons, non-linear optics, and Smith-Purcell radiation, among others. The strategies examined include the growth and processing of 2D materials, the use of various 2D materials like semiconductors, semimetals, Weyl-semimetals and 2D heterostructures or mixed-dimensional hybrid structures, and the engineering of light-matter interactions through nanophotonics, metasurfaces, and 2D polaritons. Finally, we give an outlook on the challenges in realizing high-performance and ambient-stable devices and the prospects for future research and large-scale commercial applications.

Strong, anisotropic, layer-independent second harmonic generation in multilayer SnS film

Materials based on group IV chalcogenides exhibit extensive technologically important properties. Its unusual chemical bonding and off-centering of in-layer sublattices could cause chemical polarity and weakly broken symmetry, making optical field controlling feasible. Here, we fabricated large-area SnS multilayer films and observed unexpected strong SHG response at 1030 nm. The appreciable SHG intensities were obtained with an independence on layer, which is opposite to the generation principle of overall nonzero dipole moment only in odd-layer material. Taking GaAs for reference, the second-order susceptibility was estimated to be 7.25 pm/V enhanced by mixed-chemical bonding polarity. Further polarization-dependent SHG intensity confirmed the crystalline orientation of SnS films. The results imply surface inversion symmetry broken and nonzero polarization field modified by metavalent bonding should be the origin of SHG responses. Our observations establish multilayer SnS as a promising nonlinear material, and will guide in design of IV chalcogenides with improved optics and photonics properties for the potential applications.

Liquid Phase Isolation of SnS Monolayers with Enhanced Optoelectronic Properties

Recent advances in atomically thin two dimensional (2D) anisotropic group IV_A -VI metal monochalcogenides (MMCs) and their fascinating intrinsic properties and potential applications are hampered due to an ongoing challenge of monolayer isolation. Among the most promising MMCs, tin (II) sulfide (SnS) is an earth-abundant layered material with tunable bandgap and anisotropic physical properties, which render it extraordinary for electronics and optoelectronics. To date, however, the successful isolation of atomically thin SnS single layers at large quantities has been challenging due to the presence of strong interlayer interactions, attributed to the lone-pair electrons of sulfur. Here, a novel liquid phase exfoliation approach is reported, which enables the overcome of such strong interlayer binding energy. Specifically, it demonstrates that the synergistic action of external thermal energy with the ultrasound energy-induced hydrodynamic force in solution gives rise to the systematic isolation of highly crystalline SnS monolayers (1L-SnS). It is shown that the exfoliated 1L-SnS crystals exhibit high carrier mobility and deep-UV spectral photodetection, featuring a fast carrier response time of 400 ms. At the same time, monolayer-based SnS transistor devices fabricated from solution present a high on/off ratio, complemented with a responsivity of 6.7 × 10^-3 A W^-1 and remarkable stability upon prolonged operation in ambient conditions. This study opens a new avenue for large-scale isolation of highly crystalline SnS and other MMC manolayers for a wide range of applications, including extended area nanoelectronic devices, printed from solution.

Low symmetric sub-wavelength array enhanced lensless polarization-sensitivity photodetector of germanium selenium

Polarization-sensitive photodetectors, with the ability of identifying the texture-, stress-, and roughness-induced light polarization state variation, displace unique advantages in the fields of national security, medical diagnosis, and aerospace. The utilization of in-plane anisotropic two-dimensional (2D) materials has led the polarization photodetector into a polarizer-free regime, and facilitated the miniaturization of optoelectronic device integration. However, the insufficient polarization ratio (usually less than 10) restricts the detection resolution of polarized signals. Here, we designed a sub-wavelength array (SWA) structure of 2D germanium selenium (GeSe) to further improve its anisotropic sensitivity, which boosts the polarized photocurrent ratio from 1.6 to 18. This enhancement comes from the combination of nano-scale arrays with atomic-scale lattice arrangement at the low-symmetric direction, while the polarization-sensitive photoresponse along the high-symmetric direction is strongly suppressed due to the SWA-caused depolarization effect. Our mechanism study revealed that the SWA can improve the asymmetry of charge distribution, attenuate the matrix element in zigzag direction, and the localized surface plasma, which elevates the photo absorption and photoelectric transition probability along the armchair direction, therefore accounts for the enhanced polarization sensitivity. In addition, the photodetector based on GeSe SWA exhibited a broad power range of 40 dB at a near-infrared wavelength of 808 nm and the ability of weak-light detection under 0.1 LUX of white light (two orders of magnitude smaller than pristine 2D GeSe). This work provides a feasible guideline to improve the polarization sensitivity of 2D materials, and will greatly benefit the development of polarized imaging sensors.

Ultrathin ferrite nanosheets for room-temperature two-dimensional magnetic semiconductors

The discovery of magnetism in ultrathin crystals opens up opportunities to explore new physics and to develop next-generation spintronic devices. Nevertheless, two-dimensional magnetic semiconductors with Curie temperatures higher than room temperature have rarely been reported. Ferrites with strongly correlated d-orbital electrons may be alternative candidates offering two-dimensional high-temperature magnetic ordering. This prospect is, however, hindered by their inherent three-dimensional bonded nature. Here, we develop a confined-van der Waals epitaxial approach to synthesizing air-stable semiconducting cobalt ferrite nanosheets with thickness down to one unit cell using a facile chemical vapor deposition process. The hard magnetic behavior and magnetic domain evolution are demonstrated by means of vibrating sample magnetometry, magnetic force microscopy and magneto-optical Kerr effect measurements, which shows high Curie temperature above 390 K and strong dimensionality effect. The addition of room-temperature magnetic semiconductors to two-dimensional material family provides possibilities for numerous novel applications in computing, sensing and information storage.

Van der Waals crystals allow for magnetism down to the monolayer limit, however, this magnetism, and frequently the material itself, is fragile. Ferrites, conversely, have robust material stability and magnetic order, but are three dimensional. Here the authors succeed in creating a single unit cell thickness of Cobalt Ferrite via chemical vapour deposition, with hard magnetic properties, and curie temperature exceeding room temperature.

Liquid-Phase Exfoliation of Bismuth Telluride Iodide (BiTeI): Structural and Optical Properties of Single-/Few-Layer Flakes

Bismuth telluride halides (BiTeX) are Rashba-type crystals with several potential applications ranging from spintronics and nonlinear optics to energy. Their layered structures and low cleavage energies allow their production in a two-dimensional form, opening the path to miniaturized device concepts. The possibility to exfoliate bulk BiTeX crystals in the liquid represents a useful tool to formulate a large variety of functional inks for large-scale and cost-effective device manufacturing. Nevertheless, the exfoliation of BiTeI by means of mechanical and electrochemical exfoliation proved to be challenging. In this work, we report the first ultrasonication-assisted liquid-phase exfoliation (LPE) of BiTeI crystals. By screening solvents with different surface tension and Hildebrandt parameters, we maximize the exfoliation efficiency by minimizing the Gibbs free energy of the mixture solvent/BiTeI crystal. The most effective solvents for the BiTeI exfoliation have a surface tension close to 28 mN m^-1 and a Hildebrandt parameter between 19 and 25 MPa^0.5. The morphological, structural, and chemical properties of the LPE-produced single-/few-layer BiTeI flakes (average thickness of ∼3 nm) are evaluated through microscopic and optical characterizations, confirming their crystallinity. Second-harmonic generation measurements confirm the non-centrosymmetric structure of both bulk and exfoliated materials, revealing a large nonlinear optical response of BiTeI flakes due to the presence of strong quantum confinement effects and the absence of typical phase-matching requirements encountered in bulk nonlinear crystals. We estimated a second-order nonlinearity at 0.8 eV of |χ⁽²⁾| ∼ 1 nm V^-1, which is 10 times larger than in bulk BiTeI crystals and is of the same order of magnitude as in other semiconducting monolayers (e.g., MoS₂).

Nonlinear Optical and Photocurrent Responses in Janus MoSSe Monolayer and MoS2-MoSSe van der Waals Heterostructure

Two-dimensional (2D) transition metal dichalcogenides are promising materials platforms for a variety of optoelectronic device applications. Janus 2D materials are a rising class of 2D materials with low symmetry, which leads to the emergence of out-of-plane electric polarization and piezoelectricity. Using first-principles density functional theory, we show that monolayer and bilayer heterostructure Janus MoSSe moieties exhibit strong nonlinear optical responses that are vanishing in the non-Janus form. The absence of horizontal mirror plane symmetry enables a circular photocurrent as well as a large out-of-plane second harmonic generation (SHG) and shift photocurrent. Through a comparative study of the Janus heterostructure MoS₂-MoSSe on five distinct stacking configurations, we find that the magnitude of the out-of-plane SHG in the Janus heterostructure is enhanced due to the interlayer coupling and interference effect compared to that of monolayer MoSSe. Thus, Janus 2D materials offer a unique opportunity for exploring nonlinear optical phenomena and designing configurable layered nonlinear optical materials.

Sliding Modulation in Nonlinear Optical Effect in Two-Dimensional van der Waals Cu2MoS4

Owing to different nonlinear optical (NLO) motifs with diverse structural and symmetrical assemblies, two-dimensional (2D) van der Waals (vdW) transition metal ternary chalcogenides (TMTCs) have unique advantages in nano-NLO modulation compared to 2D vdW transition metal dichalcogenides (e.g., MoS₂). Based on first-principles calculations, in this study, we discover that layered Cu₂MoS₄ with two tetrahedral [MoS₄] and [CuS₄] motifs, as a representative 2D vdW TMTC, has an extremely rare sliding-modulated second harmonic effect with nearly 70% fluctuation, much larger than 5% in MoS₂ with a single octahedral [MoS₆] motif because of different synergistic effects among intra- and interlayer NLO polarizations induced by the [CuS₄] and [MoS₄] NLO-active motifs. Furthermore, the Cu₂MoS₄ layers exhibit a low energy barrier in interlayer sliding with a robust SHG response against large strains, displaying a novel and applicable NLO-modulation mechanism in nano-optoelectronics.

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.

First-Principles Study of the Structural, Electronic, and Enhanced Optical Properties of SnS/TaS2 Heterojunction

Although the electronics and optoelectronics based on two-dimensional (2D) SnS have attracted great interest, their development is hindered by the large contact resistance at the interface of the metal-semiconductor junction. In this work, using first-principles calculations, we evaluate the contact performance in a van der Waals heterostructure composed of 2D SnS and TaS₂. We demonstrate that holes can freely transfer from the electrode to the channel as a consequence of the Schottky-barrier-free interface as well as an upward band bending. Moreover, we show that the intrinsic properties of the SnS monolayer are well-preserved in the heterojunction, which is different from those of contact with metal surfaces. An enhanced optical response is also observed as compared with the freestanding sheet. Given the recent experimental synthesis of the SnS-TaS₂ superlattice, this study enhances the understanding of the interface properties of SnS-based metal contact, which is essential for future device applications.

Two-dimensional multiferroics

Due to unprecedented application prospects such as high-density and low-power multistate storage, spintronics and nanoelectronics, two-dimensional (2D) multiferroics, coupled with at least two ferroic orders, have gotten a lot of interest in recent years. Multiple functions can be achieved in 2D multiferroics via coupling phenomena such as magnetoelectricity, piezoelectricity, and magnetoelasticity, which offers technical support for the creation of multifunctional devices. The research progress of 2D ferromagnetic-ferroelectric multiferroic materials, ferroelectric-ferroelastic multiferroic materials, and ferromagnetic-ferroelastic materials in recent years is reviewed in this paper. The categorization of 2D multiferroics is explored in terms of the multiple sources of ferroelectricity. The top-down approaches and the bottom-up methods used to fabricate 2D multiferroics materials are introduced. Finally, the authors outline potential research prospects and application scenarios for 2D multiferroic materials.

Room-Temperature Ferroelectricity in 2D Metal-Tellurium-Oxyhalide Cd7Te7Cl8O17 via Selenium-Induced Selective-Bonding Growth

Two-dimensional (2D) ferroelectric materials have attracted increasing interest due to meeting the requirements of integration, miniaturization, and multifunction of devices. However, the exploration of intrinsic 2D ferroelectric materials is still in the early stage, for which the related reports are still limited, especially fewer ones prepared by chemical vapor deposition (CVD). Here, the ultrathin metal-tellurium-oxyhalide Cd₇Te₇Cl₈O₁₇ (CTCO) flakes as thin as 3.8 nm are realized via the selenium-induced selective-bonding CVD method. The growth mechanism has been confirmed by experiments and theoretical calculations, which can be ascribed to the induction of selective bonding of a hydrogen atom in H₂O molecules by the introduction of selenium, leading to the generation of strong oxidants. Excitingly, switchable out-of-plane ferroelectric polarization was observed in CTCO flakes down to 6 nm at room temperature, which may be caused by mobile Cl vacancies. This work has implications for the synthesis and applications of 2D ferroelectric materials.

Two-Dimensional Materials with Giant Optical Nonlinearities near the Theoretical Upper Limit

Nonlinear optical (NLO) phenomena such as harmonic generation and Kerr and Pockels effects are of great technological importance for lasers, frequency converters, modulators, switches, etc. Recently, two-dimensional (2D) materials have drawn significant attention due to their strong and peculiar NLO properties. Here, we describe an efficient first-principles workflow for calculating the quadratic optical response and apply it to 375 non-centrosymmetric semiconductor monolayers from the Computational 2D Materials Database (C2DB). Sorting the nonresonant nonlinearities with respect to bandgap E_g reveals an upper limit proportional to E_g^-4, which is neatly explained by two distinct generic models. We identify multiple promising candidates with giant nonlinearities and bandgaps ranging from 0.4 to 5 eV, some of which approach the theoretical upper limit and greatly outperform known materials. Our comprehensive library of ab initio NLO spectra for all 375 monolayers is freely available via the C2DB Web site.

Stacking-Engineered Heterostructures in Transition Metal Dichalcogenides

The layer-by-layer assembly of 2D transition metal dichalcogenide monolayer blocks to form a 3D stack, with a precisely chosen sequence/angle, is the newest development for these materials. In this way, one can create "van der Waals heterostructures (HSs)," opening up a new realm of materials engineering and novel devices with designed functionalities. Herein, a detailed systematic review of transition metal dichalcogenide stacking-engineered heterostructures, from controllable fabrication to typical characterization, and stacking-correlated physical behaviors is presented. Furthermore, recent advances in stacking design, such as stacking sequence, twist angles, and moiré superlattice heterojunctions, are also comprehensively summarized. Finally, the remaining challenges and possible strategies for using stacking engineering to tune the properties of 2D materials are also outlined.

Significant second-harmonic generation and bulk photovoltaic effect in trigonal selenium and tellurium chains

One-dimensional (1D) selenium and tellurium crystalize in helical chainlike structures and thus exhibit fascinating properties. By performing first-principles calculations, we have researched the linear and nonlinear optical (NLO) properties of 1D Se and Te, and find that both systems exhibit pronounced NLO responses. In particular, 1D Se is found to possess a large second-harmonic generation coefficient with the χ value being up to 7 times larger than that of GaN, and is even several times larger than that of the bulk counterpart. On the other hand, 1D Te also produces significant NLO susceptibility χ which exceeds that of bulk GaN by 5 times. Furthermore, 1D Te is shown to possess a prominent linear electro-optic coefficient r_xxx(0). In particular, the Te chain exhibits a large shift current response and the maximum is twice as large as the maximal photovoltaic responses obtained from BaTiO₃. Therefore, 1D Se and Te may find potential applications in solar energy conversion, electro-optical switches, and so on. Finally, the much stronger NLO effects of 1D Se and Te are attributed to their one-dimensional structures with high anisotropy, strong covalent bonding and lone-pair electrons. These findings will contribute further to experimental studies and the search for excellent materials with large NLO effects.

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.

Giant nonlinear optical activity in two-dimensional palladium diselenide

Nonlinear optical effects in layered two-dimensional transition metal chalcogenides have been extensively explored recently because of the promising prospect of the nonlinear optical effects for various optoelectronic applications. However, these materials possess sizable bandgaps ranging from visible to ultraviolet region, so the investigation of narrow-bandgap materials remains deficient. Here, we report our comprehensive study on the nonlinear optical processes in palladium diselenide (PdSe₂) that has a near-infrared bandgap. Interestingly, this material exhibits a unique thickness-dependent second harmonic generation feature, which is in contrast to other transition metal chalcogenides. Furthermore, the two-photon absorption coefficients of 1–3 layer PdSe₂ (β ~ 4.16 × 10⁵, 2.58 × 10⁵, and 1.51 × 10⁵ cm GW⁻¹) are larger by two and three orders of magnitude than that of the conventional two-dimensional materials, and giant modulation depths (α_s ~ 32%, 27%, and 24%) were obtained in 1–3 layer PdSe₂. Such unique nonlinear optical characteristics make PdSe₂ a potential candidate for technological innovations in nonlinear optoelectronic devices.

Strong nonlinearities in 2D materials can lead to interesting applications in optoelectronics. Here the authors investigate the optical nonlinearity of palladium diselenide, determine the layer dependent two photon absorption efficiency and the saturable absorption modulation depth.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Perovskite-Derivative Valleytronics

Halide perovskites are revolutionizing the renewable energy sector owing to their high photovoltaic efficiency, low manufacturing cost, and flexibility. Their remarkable mobility and long carrier lifetime are also valuable for information technology, but fundamental challenges like poor stability under an electric field prevent realistic applications of halide perovskites in electronics. Here, it is discovered that valleytronics is a promising route to leverage the advantages of halide perovskites and derivatives for information storage and processing. The synthesized all-inorganic lead-free perovskite derivative, Cs₃ Bi₂ I₉ , exhibits strong light-matter interaction and parity-dependent optically addressable valley degree of freedom. Robust optical helicity in all odd-layer-number crystals with inversion symmetry breaking is observed, indicating excitonic coherence extending well beyond 11 layers. The excellent optical and valley properties of Cs₃ Bi₂ I₉ arise from the unique parallel bands, according to first principles calculations. This discovery points to new materials design principles for scalable valleytronic devices and demonstrates the promise of perovskite derivatives beyond energy applications.

Direct Measurement of Folding Angle and Strain Vector in Atomically Thin WS2 Using Second-Harmonic Generation

Structural engineering techniques such as local strain engineering and folding provide functional control over critical optoelectronic properties of 2D materials. Local strain engineering at the nanoscale level is practically achieved via permanently deformed wrinkled nanostructures, which are reported to show photoluminescence enhancement, bandgap modulation, and funneling effect. Folding in 2D materials is reported to tune optoelecronic properties via folding angle dependent interlayer coupling and symmetry variation. The accurate and efficient monitoring of local strain vector and folding angle is important to optimize the performance of optoelectronic devices. Conventionally, the accurate measurement of both strain amplitude and strain direction in wrinkled nanostructures requires the combined usage of multiple tools resulting in manufacturing lead time and cost. Here, we demonstrate the usage of a single tool, polarization-dependent second-harmonic generation (SHG), to determine the folding angle and strain vector accurately and efficiently in ultrathin WS₂. The folding angle in trilayer WS₂ folds exhibiting 1-9 times SHG enhancement is probed through variable approaches such as SHG enhancement factor, maxima and minima SHG phase difference, and linear dichroism. In compressive strain induced wrinkled nanostructures, strain-dependent SHG quenching and enhancement is observed parallel and perpendicular, respectively, to the direction of the compressive strain vector, allowing us to determine the local strain vector accurately using a photoelastic approach. We further demonstrate that SHG is highly sensitive to band-nesting-induced transition (C-peak), which can be significantly modulated by strain. Our results show SHG as a powerful probe to folding angle and strain vector.

Recent Advances in 2D Metal Monochalcogenides

The family of emerging low-symmetry and structural in-plane anisotropic two-dimensional (2D) materials has been expanding rapidly in recent years. As an important emerging anisotropic 2D material, the black phosphorene analog group IVA-VI metal monochalcogenides (MMCs) have been surged recently due to their distinctive crystalline symmetries, exotic in-plane anisotropic electronic and optical response, earth abundance, and environmentally friendly characteristics. In this article, the recent research advancements in the field of anisotropic 2D MMCs are reviewed. At first, the unique wavy crystal structures together with the optical and electronic properties of such materials are discussed. The Review continues with the various methods adopted for the synthesis of layered MMCs including micromechanical and liquid phase exfoliation as well as physical vapor deposition. The last part of the article focuses on the application of the structural anisotropic response of 2D MMCs in field effect transistors, photovoltaic cells nonlinear optics, and valleytronic devices. Besides presenting the significant research in the field of this emerging class of 2D materials, this Review also delineates the existing limitations and discusses emerging possibilities and future prospects.

The partition principles for atomic-scale structures and their physical properties: application to the nonlinear optical crystal material KBe2BO3F2

In implementing the materials genome approach to search for new materials with interesting properties or functions, it is necessary to find the correct functional motif. To this end, it is common to partition an extended structure into various building units and then partition its properties to find the appropriate functional motif. We have developed the general principles for partitioning a structure and its properties in terms of a set of atoms and bonds by analyzing the differential cross-sections of neutron and X-ray scattering phenomena and proposed the procedures with which to partition an extended structure and its properties. We demonstrate how these procedures work by analyzing the nonlinear optical crystal KBe2BO3F2. Our partitioning analysis of KBe2BO3F2 leads to the conclusion that the second harmonic generation response of KBe2BO3F2 is dominated by the ionically bonded metal-centered groups.

Tunable anisotropic plasmon response of monolayer GeSe nanoribbon arrays

Recently, emerging two-dimensional (2D) germanium selenide (GeSe) has drawn lots of attention due to its in-plane anisotropic properties and great potential for optoelectronic applications such as in solar cells. However, methods are still sought to enhance its interaction with light to enable practical applications. Herein, we numerically investigate the localized plasmon response of monolayer GeSe nanoribbon arrays systematically, and the results show that localized surface plasmon polaritons in the far-infrared range with anisotropic behavior can be efficiently excited to enhance the light-matter interaction. We further show that the plasmon response of monolayer GeSe nanoribbons could be tuned effectively through the nanoribbon width, local refractive index, substrate thickness and carrier concentration, pointing out the ways for controlling the localized plasmon response. In the case of monolayer GeSe nanoribbons on a substrate of finite thickness, a Fabry-Pérot-like (FP-like) quantitative model has been proposed to explain the overall spectral response originating from overlapped FP and plasmon modes, and it matches well with the simulation results. All in all, we investigate the plasmon response of the novel 2D GeSe nanoribbons thoroughly for the first time, bringing opportunities for potential applications of novel polarization-dependent optoelectronic devices.

Purely in-plane ferroelectricity in monolayer SnS at room temperature

2D van der Waals ferroelectrics have emerged as an attractive building block with immense potential to provide multifunctionality in nanoelectronics. Although several accomplishments have been reported in ferroelectric switching for out-of-plane ferroelectrics down to the monolayer, a purely in-plane ferroelectric has not been experimentally validated at the monolayer thickness. Herein, an in-plane ferroelectricity is demonstrated for micrometer-size monolayer SnS at room temperature. SnS has been commonly regarded to exhibit the odd–even effect, where the centrosymmetry breaks only in the odd-number layers to exhibit ferroelectricity. Remarkably, however, a robust room temperature ferroelectricity exists in SnS below a critical thickness of 15 layers with both an odd and even number of layers, suggesting the possibility of controlling the stacking sequence of multilayer SnS beyond the limit of ferroelectricity in the monolayer. This work will pave the way for nanoscale ferroelectric applications based on SnS as a platform for in-plane ferroelectrics.

Out-of-plane ferroelectricity is usually unstable in the two dimensional limit due to the presence of the depolarization field. Here, the authors successfully circumvent this issue by growing µm-sized SnS monolayers that exhibit in-plane ferroelectricity that is stable at room temperature.

Second harmonic generation in Janus MoSSe a monolayer and stacked bulk with vertical asymmetry

A recently synchronized Janus TMD material with broken out-of-plane symmetry offers a vertical dipole to enhance nonlinear optical behavior. Here, by comparing the second harmonic generation properties of MoS₂ and MoSSe monolayers, we investigated the nonzero out-of-plane SHG susceptibilities of a Janus MoSSe 2D material. A three-fold enhancement of out-of-plane SHG susceptibilities exists in three stacked bulks of Janus MoSSe compared to that in the monolayer. A sensitivity to their stack pattern is also found. The broken out-of-plane symmetry, vertical dipole, and intrinsic tunable electronic properties of Janus two-dimensional materials make MoSSe a promising nanomaterial for nonlinear optical devices.

Ferroicity-driven nonlinear photocurrent switching in time-reversal invariant ferroic materials

Nonlinear optical responses to external electromagnetic field, characterized by second- and higher-order susceptibilities, play crucial roles in nonlinear optics and optoelectronics. Here, we demonstrate the possibility to achieve ferroicity-driven nonlinear photocurrent switching in time-reversal invariant multiferroics. It is enabled by the second-order current response to electromagnetic field whose direction can be controlled by both internal ferroic orders and external light polarization. Second-order direct photocurrent consists of shift current and circular photocurrent under linearly and circularly polarized light irradiation, respectively. We elucidate the microscopic mechanism in a representative class of two-dimensional multiferroic materials using group theoretical analyses and first-principles theory. The complex interplay of symmetries, shift vector, and Berry curvature governs the fundamental properties and switching behavior of shift current and circular photocurrent. Ferroicity-driven nonlinear photocurrent switching will open avenues for realizing nonlinear optoelectronics, nonlinear multiferroics, etc., using the coupled ferroic orders and nonlinear responses of ferroic materials under external field.

Recent progress in 2D group IV-IV monochalcogenides: synthesis, properties and applications

Coordination-related, 2D structural phase transitions are a fascinating facet of 2D materials with structural degeneracy. Phosphorene and its new phases, exhibiting unique electronic properties, have received considerable attention. The 2D group IV-IV monochalcogenides (i.e. GeS, GeSe, SnS and SnSe) like black phosphorous possess puckered layered orthorhombic structure. The 2D group IV-IV monochalcogenides with advantages of earth-abundance, less toxicity, environmental compatibility and chemical stability, can be widely used in optoelectronics, piezoelectrics, photodetectors, sensors, Li-batteries and thermoelectrics. In this review, we summarized recent research progress in theory and experiment, which studies the fundamental properties, applications and fabrication of 2D group IV-IV monochalcogenides and their new phases, and brings new perspectives and challenges for the future of this emerging field.

Ultrafast Zero-Bias Surface Photocurrent in Germanium Selenide: Promise for Terahertz Devices and Photovoltaics

Theory predicts that a large spontaneous electric polarization and concomitant inversion symmetry breaking in GeSe monolayers result in a strong shift current in response to their excitation in the visible range. Shift current is a coherent displacement of electron density on the order of a lattice constant upon above-bandgap photoexcitation. A second-order nonlinear effect, it is forbidden by the inversion symmetry in the bulk GeSe crystals. Here, we use terahertz (THz) emission spectroscopy to demonstrate that ultrafast photoexcitation with wavelengths straddling both edges of the visible spectrum, 400 and 800 nm, launches a shift current in the surface layer of a bulk GeSe crystal, where the inversion symmetry is broken. The direction of the surface shift current determined from the observed polarity of the emitted THz pulses depends only on the orientation of the sample and not on the linear polarization direction of the excitation. Strong absorption by the low-frequency infrared-active phonons in the bulk of GeSe limits the bandwidth and the amplitude of the emitted THz pulses. We predict that reducing GeSe thickness to a monolayer or a few layers will result in a highly efficient broadband THz emission. Experimental demonstration of THz emission by the surface shift current in bulk GeSe crystals puts this 2D material forward as a candidate for next-generation shift current photovoltaics, nonlinear photonic devices, and THz sources.

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.

Nonlinear Optics with 2D Layered Materials

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented.

Mechanisms of Pyroelectricity in Three- and Two-Dimensional Materials

Pyroelectricity is a very promising phenomenon in three- and two-dimensional materials, but first-principles calculations have not so far been used to elucidate the underlying mechanisms. Here we report density-functional theory (DFT) calculations based on the Born-Szigeti theory of pyroelectricity, by combining fundamental thermodynamics and the modern theory of polarization. We find satisfactory agreement with experimental data in the case of bulk benchmark materials, showing that the so-called electron-phonon renormalization, whose contribution has been traditionally viewed as negligible, is important. We predict out-of-plane pyroelectricity in the recently synthesized Janus MoSSe monolayer and in-plane pyroelectricity in the group-IV monochalcogenide GeS monolayer. It is notable that the so-called secondary pyroelectricity is found to be dominant in GeS monolayer. The present work opens a theoretical route to study the pyroelectric effect using DFT and provides a valuable tool in the search for new candidates for pyroelectric applications.