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

Second-harmonic generation in 2D moiré superlattices composed of bilayer transition metal dichalcogenides

Moiré superlattices (MSLs) in twisted two-dimensional van der Waals materials feature twist-angle-dependent crystal symmetry and strong optical nonlinearities. By adjusting the twist angle in bilayer van der Waals materials, the second-harmonic generation (SHG) can be controlled. Here, we focus on exploring the electronic and SHG properties of MSLs in 2D bilayer transition metal dichalcogenides (TMDs) with different twist angles through first-principles calculations. We constructed MSL structures of five TMD materials, including three single-phase materials (MoS2, WS2, and MoSe2) and two heterojunctions (MoS2/MoSe2 and MoS2/WS2) with twist angles of 9.4°, 13.2°, 21.8°, 32.2°, and 42.1° without lattice mismatch. Our findings demonstrate a consistent variation in the SHG susceptibility among different TMD MSLs as a response to twist-angle changes. The underlying reason for the twist-angle dependence of SHG is that the twist angle regulates the interlayer coupling strength, affecting the optical band gap of MSLs and subsequently tuning the SHG susceptibility. Through a comparison of the static SHG susceptibility values, we identified the twist angle of 9.4° as the configuration that yields the highest SHG susceptibility (e.g. 358.5 pm V-1 for the 9.4° MoSe2 MSL). This value is even twice that of the monolayer (173.3 pm V-1 for monolayer MoSe2) and AA'-stacked bilayer structures (139.8 pm V-1 for AA' MoSe2). This high SHG susceptibility is attributed to the strong interlayer coupling in the 9.4° MSL, which enhances the valence band energy (contributed by the antibonding orbitals of chalcogen-pz and transition metal-dz2) and consequently leads to a small optical band gap, thus improving the optical transitions. The findings of this study provide a straightforward way to improve the SHG performance of bilayer TMDs and also throw light on the sensitive relationship between the twist angle, band structure and SHG properties of TMD MSLs.

Nonlinear Optical Activities in Two-Dimensional Gallium Sulfide: A Comprehensive Study

The nonlinear optical (NLO) properties of two-dimensional (2D) materials are fascinating for fundamental physics and optoelectronic device development. However, relatively few investigations have been conducted to establish the combined NLO activities of a 2D material. Herein, a study of numerous NLO properties of 2D gallium sulfide (GaS), including second-harmonic generation (SHG), two-photon excited fluorescence (TPEF), and NLO absorption are presented. The layer-dependent SHG response of 2D GaS identifies the noncentrosymmetric nature of the odd layers, and the second-order susceptibility (χ²) value of 47.98 pm/V (three-layers of GaS) indicates the superior efficiency of the SHG signal. In addition, structural deformation induces the symmetry breaking and facilitates the SHG in the bulk samples, whereas a possible efficient symmetry breaking in the liquid-phase exfoliated samples results in an enhancement of the SHG signal, providing prospective fields of investigation for researchers. The generation of TPEF from 800 to 860 nm depicts the two-photon absorption characteristics of 2D GaS material. Moreover, the saturable absorption characteristics of 2D GaS are realized from the largest nonlinear absorption coefficient (β) of -9.3 × 10³, -91.0 × 10³, and -6.05 × 10³ cm/GW and giant modulation depths (T_s) of 24.4%, 35.3%, and 29.1% at three different wavelengths of 800, 1066, and 1560 nm, respectively. Hence, such NLO activities indicate that 2D GaS material can facilitate in the technical advancements of future nonlinear optoelectronic devices.

Anomalous polarization pattern evolution of Raman modes in few-layer ReS2 by angle-resolved polarized Raman spectroscopy

Low-symmetry of ReS₂ has not only in-plane but also out-of-plane anisotropic light scattering, which is complicated, yet interesting with intrinsic strong electron-phonon coupling. In such a case, the Raman tensor also gets sophisticated with nine non-zero elements, which is layer-dependent for different Raman modes. Herein, we systematically investigated the polarization pattern evolution of both in-plane and out-of-plane Raman modes of few-layer ReS₂ by angle-resolved polarized Raman spectroscopy. We found that in-plane Raman modes with less layer-dependence could be used to determine the crystal orientation (Re-chain direction) due to the weak electron-phonon interaction between layers. However, the out-of-plane and mixed vibration Raman modes demonstrate much evident layer-dependence due to the obvious electron-phonon interaction between layers. As such, the polarization patterns for the out-of-plane vibration Raman modes are distorted with layers in not only petal types but also maximum Raman intensity directions. This distortion is mainly due to the phase difference between Raman elements, which are complex values due to the near bandgap excitation laser. The results reveal that deep insights into anisotropy in low-symmetry two-dimensional materials could afford not only rich physics but also potential polarized optoelectronic devices.

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.

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.

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.

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.

HfS2/MoTe2 vdW heterostructure: bandstructure and strain engineering based on first-principles calculation

In this study, a multilayered van der Waals (vdW) heterostructure, HfS₂/MoTe₂, was modeled and simulated using density functional theory (DFT). It was found that the multilayers (up to 7 layers) are typical indirect bandgap semiconductors with an indirect band gap varying from 0.35 eV to 0.51 eV. The maximum energy value of the valence band (VBM) and the minimum energy value of the conduction band (CBM) of the heterostructure were found to be dominated by the MoTe₂ layer and the HfS₂ layer, respectively, characterized as type-II band alignment, leading to potential photovoltaic applications. Optical spectra analysis also revealed that the materials have strong absorption coefficients in the visible and ultraviolet regions, which can be used in the detection of visible and ultraviolet light. Under an external strain perpendicular to the layer plane, the heterostructure exhibits a general transition from semiconductor to metal at a critical interlayer-distance of 2.54 Å. The carrier effective mass and optical properties of the heterostructures can also be modulated under external strain, indicating a good piezoelectric effect in the heterostructure.

Direct Observation of Charge Injection of Graphene in the Graphene/WSe2 Heterostructure by Optical-Pump Terahertz-Probe Spectroscopy

Charge transfer across the interface and interlayer coupling in the graphene van der Waals heterostructure, which is constructed by graphene and semiconducting transition metal dichalcogenides (TMDCs), is critical for their electronic and optoelectronic applications. Photo-induced charge injection from TMDC to graphene has been studied in several heterostructure photodetectors. However, the response time significantly varies among different reports, ranging from microseconds to milliseconds. In this work, using a graphene/WSe₂ heterostructure as an example, we directly observe the carrier density change in graphene by time-resolved optical-pump terahertz (THz)-probe spectroscopy and show the ultrafast picosecond photoresponse of graphene. In the absence of photoexcitation, THz time-domain spectroscopic measurements show that WSe₂ can transfer holes to graphene and pull down the Fermi level of graphene. After excitation by the ultrafast laser pulse, the transient THz response shows a rapid (∼0.35 ps) increase in the graphene conductivity mainly due to the hole injection from WSe₂ into graphene. Unlike previous reports on band bend as the guidance mechanism for charge transfer, our results show that the relevant mechanism is the band offset across the atomically sharp interface.