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

Abstract

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 d 16 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.

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

“…The magnitudes of these nonlinear coefficients for WS 2 and GaSe are comparable to that of group IV monochalcogenides such as GeSe, GeS, SnSe, and SnS . The prominent peaks in the dispersion of the second-order nonlinear coefficients for unstrained WS 2 and GaSe monolayers are mainly caused by transitions from the high-symmetry point and the high-symmetry line in the band structure. ,,,− The multiple-peak resonance of second-order nonlinear coefficients at high photon energy (especially above the band gap) arises from band nesting in WS 2 and GaSe monolayers. , According to energy matching, the correlation between the second-order nonlinear coefficient and the electronic structure can be determined by the two-photon transition. , The relationship d 16 = d 21 = − d 22 breaks down for strained WS 2 and GaSe due to uniaxial-strain-induced in-plane anisotropy. In the previous work, the biaxial strain could not break the in-plane symmetry, resulting in the unchanged nonlinear coefficient relationship in 2D MXenes .…”

“…In particular, second-harmonic generation (SHG) as an essential second-order nonlinear optical effect is widely used to characterize the nonlinear optical properties of 2D materials and in turn for high-efficient on-chip frequency conversion. − Therefore, tuning the SHG properties of 2D materials is desirable for the optimization of the nonlinear optical performance of optoelectronic devices. Currently, several ways have been developed to engineer the nonlinear optical properties of 2D materials such as heterostructure design, ,− electrical control, − temperature control, , defect engineering, wavelength control, − stacking order control, ,,− 2D material/metasurface hybridization, − 2D materials on an epsilon-near-zero substrate, structural engineering by nanoscroll, nanotubes, integration with nanowires or quantum dots, as well as strain engineering. ,,,,,− In these methods, strain engineering can directly change the lattice constant of 2D materials, control the SHG intensity, and tune the SHG pattern. ,, There are two kinds of strain engineering methods. One is the biaxial strain method, and the other is the uniaxial strain method. ,,, Compared with biaxial strain, uniaxial strain is an intrinsic anisotropic method for the sensitive in-plane symmetry engineering for 2D materials, which could introduce large flexibility and...…”

Accurately Controlling Angle-Resolved Second Harmonic Generation by Stacking Orders from a MoS2 Homobilayer

“…The value of the second-order nonlinear coefficient d 16 element of AA′_Mo-60 stacking near the I peak is larger than that of AA stacking because the interlayer coupling strength of AA′_Mo-60 is greater than that of AA stacking. In the dispersion relation of the second-order nonlinear coefficients for the AA and AA′_Mo-60 stackings, the other significant peaks originate from a transition through a two-photon excitation at high symmetry points or high symmetry lines in the band structure. − For the AA and AA′_Mo-60 stackings, the d 16 element can reach several hundred picometers per volt, which is on the same order of magnitude as the other stacked 2D materials − such as MoTe 2 /WSe 2 and MoSe 2 /WSe 2 heterostructures. Besides, the other nonlinear elements (including d 15 , d 31 , and d 33 ) of the AA′_Mo-60 stacked MoS 2 homobilayer can reach several tens of picometers per volt.…”

“…In this case, the symmetry of materials can be predicted by calculating the second-order nonlinear coefficient elements for an artificially stacked material. 45,48 The SHG response is determined by coupling the optical field E and the second-order nonlinear coefficient tensor d as illustrated in eq 1. 45,48…”

“…Here, T i,f , T j,g , and T k,h are elements in T(ϕ). By substituting eqs 2−4 into eq 1, the second harmonic polarization (P x , P y , P z ) can be given as follows 45,48…”