Fig. 1 Schematic diagram of SHG in stacked 2D materials

Fig. 2 Schematic diagram of 2D material stacking engineering

Fig. 3 SHG characterization of stacking layers[19-22] (a) Schematic crystal structures of 2H-MoS2 and 3R-MoS2[19]; (b) Relationship between second-harmonic (SH) intensity and layer number for 2H-MoS2 and 3R-MoS2 (SH intensity of 3R-MoS2 follows an approximate quadratic dependence, whereas that of 2H-MoS2 oscillates with changing layer number)[19]; (c) SHG image of 2H-MoS2, where pronounced signal intensity is observed only in odd-numbered layers such as monolayer, trilayer, and five-layer samples[20]; (d) Comparison of SHG intensity variations for 2H-MoS2 with different thicknesses[20]; (e) Comparison of SHG signal intensity between h-BN and 2H-MoS2[20]; (f) Schematic crystal structures of β-GaSe and ε-GaSe[22-23]; (g) Relationship between SHG intensity and layer number for β-GaSe and ε-GaSe[22]; (h) SHG signal distribution of GaSe nanosheets with different thicknesses[22]

Fig. 4 Correlation between SHG signal intensity and stacking order[25-26] (a) Different stacking structures of graphene and their corresponding SHG signal intensities[26]; (b) SHG microscopy image of ABA-stacked and ABC-stacked graphene[26]; (c) Various stacking configurations of h-BN along with the corresponding dark-field transmission electron microscopy and SHG microscopy images[25]; (d) SHG signal intensities of h-BN with different stacking configurations[25]

Fig. 5 Second-order nonlinear coefficients and angle-resolved SHG patterns of MoS2 homobilayers with different stacking orders[24] (a, b) Top and side views of the atomic structures of two typical stacking sequences in MoS2 homobilayers; (c) d16, d21 and d22 coefficients of AA-stacked and AA′_Mo-60 -stacked MoS2 homobilayers; (d) d15, d24, d31, d32 and d33 coefficients of AA′_Mo-60-stacked MoS2 homobilayers; (e, f) Angle-resolved SHG patterns of (e) AA-stacked and (f) AA′_Mo-60-stacked MoS2 homobilayers under a pump polarization angle of 0° and an incident angle of 60°

Fig. 6 SHG characterization of interlayer twist angles[27,29] (a, b) Total SHG signal (without an analyzer) of two overlapping WS2 monolayers in the region of interest (ROI), and a magnified view of the total SH intensity within the selected ROI (three points of interest (POIs) are marked in the image)[29]; (c-f) Polar plots of the SHG intensities at the three POIs[29]; (g, h) Armchair orientation imaging within the ROI and the spatial distribution map of the twist angle in the overlapping region of the two WS2 monolayers[29]; (i) Variation of the SHG signal of bilayer WSe2 as a function of twist angle (θ), where the vertical axis represents the excitation laser’s central photon energy Eex, and the horizontal axis represents the emitted SHG photon energy Eem (color scale indicates normalized SHG intensity)[27]

Fig. 7 SHG performance of homostacked 2D materials[32,43] (a) Schematic illustration of the stacking procedure for a t(m+n) layered-graphene (LG) structure[43]; (b) SHG responses under 1064 nm excitation for monolayer MoS2 (black curve), 13°-t(1+1) LG (red curve), and 13°-t(1+2) LG (blue curve) (inset showing the log-log plots of SHG intensity versus incident laser power for the 13°-t(1+2) LG, where t denotes the twist angle, m and n represent the layer numbers of the two stacked graphene parts, and LG refers to layered graphene)[43]; (c) Schematic stacking structure of an N-layer bulk BN crystal arranged with oriented domains separated by AB interfaces[32]; (d) Optical image and (e) confocal SHG image of the device, which contains regions with thicknesses from 1 to 4 layers (N=25)[32]; (f) Dependence of SHG intensity on the number of oriented bulk BN crystal blocks in the stack (inset showing the SHG intensities for regions of different thicknesses)[32]

Fig. 8 SHG performance of heterostacked 2D materials[50-51] (a) Side-view isosurface map of the charge-density difference induced in the 2LM/1LG van der Waals heterostructure, with an isovalue of 1×10-4 e/Å3, where red regions indicate electron accumulation, while green regions indicate electron depletion[50]; (b) Optical microscope image of a 2LM/1LG van der Waals heterostructure formed by transferring bilayer MoS2 (2LM) onto monolayer graphene (1LG), and (c) the corresponding spatial SHG mapping acquired under 532 nm excitation[50]; (d) Optical microscope image of a trilayer ReS2/graphene heterostructure and (e) its corresponding SHG image[51]; (f) Schematic illustration of charge transfer between trilayer ReS2 and graphene[51]