| Two-dimensional（2D）layered nano-materials have become popular research materials in the fields of integrated electronics,photonics,and optoelectronics due to their unique physical properties.Since the traditional nonlinear crystals can hardly fully meet the needs of current novel integrated optoelectronic devices,it is very important to discover nano-materials with large nonlinear responses,which can meet the challenges of on-chip integration in the future optoelectronics.In recent years,more nonlinear optics research works have focused on 2D layered nanomaterials,which are not only beneficial to the development of basic science,but also extremely attractive for various optoelectronic device applications.As a basic nonlinear optical method,second harmonic generation（SHG）is an optical branch to study the photophysical properties of nonlinear media.Usually,the SHG information includes spectroscopy,polarization dependent patterns,and imaging,which can provide a technical platform for exploring the second-order nonlinear optical response capability,symmetry,and uniformity of materials.In such case,we have investigated the second-order nonlinear optical properties of novel layered nano-materials and related van der Waals heterostructures based on first-principles.The results can guide experiments to quantitatively analyze the SHG intensity and pattern,which will promote the development of nonlinear optics in 2D layered nano-materials,and provide theoretical basis for novel nonlinear optoelectronic devices based on 2D semiconductors.The main works and innovation points are listed as follows:（1）Uniaxial strain-induced SHG in monolayer graphene with inversion symmetry.The uniaxial strain can not only open the band gap of monolayer graphene,but also effectively break the symmetry of monolayer graphene.Under-2%uniaxial strain,the monolayer graphene has a large second-order nonlinear coefficient element d34 with a value as high as1 nm/V@1 e V.Through the derivation of the SHG response of strained graphene,it is found that the contribution of d34 element to the SHG response will be further enhanced under oblique incidence.This work provides a reference for the realization of SHG in other centrosymmetric nano-materials.（2）Strain-dependent SHG in monolayer transition metal dichalcogenides（TMDs）.The second-order nonlinear coefficient dispersion relation of monolayer WX2（X=S,Se,and Te）was calculated by the first-principles.The results suggest that the prominent peaks in the dispersion relation are due to the two-photon transition from the high-symmetry point or along the high-symmetry line.A broadband second-order nonlinear optical response is achieved by applying uniaxial strain to the monolayer WS2.The uniaxial strain can break the in-plane symmetry of 2D materials,leading to both trade-off breaking of the nonlinear coefficients and new emergent nonlinear coefficients.With the presence of uniaxial strain,a classical 6-fold azimuthal angle-dependent SHG pattern is transformed into a distorted6-fold SHG pattern.Due to the lattice symmetry breaking and the uneven charge density distribution in strained 2D materials,the SHG patterns also depend on 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.This work has been published in The Journal of Physical Chemistry Letters.（3）SHG in graphene/TMDs van der Waals heterostructures.Compared with monolayer WS2,the enhanced nonlinear optical response in the infrared band can be achieved in graphene/WS2 heterostructures,resulting from the interlayer charge transfer between graphene and WS2.The value of the second-order nonlinear coefficients of graphene/WSe2heterostructures is 1.5 times larger than that of pure monolayer WSe2 at the band gap energy of monolayer WSe2 because of the enhanced carrier generation after the heterostructures formation.This work provides a new conception for obtaining the symmetry and nonlinear optical properties of 2D van der Waals heterostructures,which promote the development of nonlinear optics of heterostructures and the design of nonlinear devices.This work has been published in The Journal of Physical Chemistry Letters.（4）SHG in type-I and type-II heterostructures.By calculating the second-order nonlinear coefficients of van der Waals heterostructures with different band alignments（type I Mo Te2/WSe2 and type II Mo Se2/WSe2）,it is found that the peaks in the d16 element dispersion relationship for both Mo Te2/WSe2 and Mo Se2/WSe2 are caused by two-photons resonance transitions,while other non-zero second-order nonlinear coefficient elements are driven by the intra-band transition processes from efficient charge transfer and ultrafast charge separation.Besides,more nonzero nonlinear coefficient elements can participate in a nonlinear response at the oblique incidence,which is beneficial to the regulation of the SHG.These results reveal that the novel van der Waals heterostructures have great potential for tunable properties such as anisotropy and dispersion relations in nonlinear optoelectronic devices.This work has been published in ACS Applied Materials&Interfaces.（5）Stacking order governed SHG in Mo S2 homobilayer.Based on first-principles,we calculated the electronic band structures and the second-order nonlinear coefficients calculations on a series of Mo S2 homobilayer with accurately controlled stacking orders.The Mo S2 homobilayers with different stacking orders have different interlayer distances.The interlayer coupling strength decreases with the increase of the interlayer distance,whereas the bandgap size of the electronic band structures increases with the increase of the interlayer distance.The second-order nonlinear coefficients of three 2H-like Mo S2homobilayers can be ignored,while two 3R-like Mo S2 homobilayers possess a larger second-order nonlinear coefficient.Therefore,the SHG disappears in all 2H-like stacked bilayer Mo S2,and possess a stronger response in all 3R-like stacked bilayer Mo S2.In addition,it was found that the 3R-like bilayer Mo S2 with different space groups exhibited similar nonlinear optical responses（the intensities were different,and the angle-dependent properties were exactly the same）under normal incidence,while the two species could be distinguished under oblique incidence.These results will provide a theoretical basis for distinguishing similar stacked bilayer van der Waals materials using SHG.This work has been published in The Journal of Physical Chemistry C. |
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